Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

The value of $cot space fraction numerator 7 pi over denominator 16 end fraction plus 2 cot space fraction numerator 3 pi over denominator 8 end fraction plus cot space fraction numerator 15 pi over denominator 16 end fraction$

4
2
-2
-4

Hint:

To find the value of the given function we will first simplify the function using trigonometric identities then at last we will put the value of the required angle to get the answer.

The correct answer is: -4

$cot space fraction numerator 7 pi over denominator 16 end fraction plus 2 cot space fraction numerator 3 pi over denominator 8 end fraction plus cot space fraction numerator 15 pi over denominator 16 end fraction equals tan open parentheses straight pi over 2 minus fraction numerator 7 straight pi over denominator 16 end fraction close parentheses plus 2 tan open parentheses straight pi over 2 minus fraction numerator 3 straight pi over denominator 2 end fraction close parentheses plus c o t open parentheses straight pi minus straight pi over 16 close parentheses space space space space open square brackets tan straight pi over 2 minus x equals c o t space x comma space c o t space straight pi minus straight x equals negative cotx close square brackets equals tan straight pi over 16 plus 2 tan straight pi over 8 minus c o t straight pi over 16 equals open parentheses tan straight pi over 16 minus c o t straight pi over 16 close parentheses plus 2 tan straight pi over 8 equals open parentheses fraction numerator sin begin display style straight pi over 16 end style over denominator cos begin display style straight pi over 16 end style end fraction minus fraction numerator cos begin display style straight pi over 16 end style over denominator sin begin display style straight pi over 16 end style end fraction close parentheses plus 2 fraction numerator sin begin display style straight pi over 8 end style over denominator cos begin display style straight pi over 8 end style end fraction equals open parentheses fraction numerator sin squared begin display style straight pi over 16 end style minus cos squared begin display style straight pi over 16 end style over denominator cos begin display style straight pi over 16 end style sin begin display style straight pi over 16 end style end fraction close parentheses plus 2 fraction numerator sin begin display style straight pi over 8 end style over denominator cos begin display style straight pi over 8 end style end fraction equals 2 fraction numerator negative cos begin display style straight pi over 8 end style over denominator sin begin display style straight pi over 8 end style end fraction plus 2 fraction numerator sin begin display style straight pi over 8 end style over denominator cos begin display style straight pi over 8 end style end fraction space space space space space space space space space space space space space space space space space space space space space space space space open square brackets cos squared x minus sin squared x equals c o x 2 x comma space 2 sin x space cos x space equals sin 2 x close square brackets equals negative 2 open parentheses fraction numerator cos squared begin display style straight pi over 8 end style minus sin squared begin display style straight pi over 8 end style over denominator sin begin display style straight pi over 8 end style cos begin display style straight pi over 8 end style end fraction close parentheses equals negative 2 open parentheses fraction numerator 2 cos begin display style straight pi over 4 end style over denominator sin begin display style straight pi over 4 end style end fraction close parentheses space space space space space space space space space space space space space space space space space space space open square brackets cos squared x minus sin squared x equals c o x 2 x comma space 2 sin x space cos x space equals sin 2 x close square brackets equals negative 4 c o t straight pi over 4 equals negative 4 cross times 1 space space space space space space space space space space space space space space open square brackets c o t straight pi over 4 equals 1 close square brackets equals negative 4$

Related Questions to study

For any real $theta$ , the maximum value of $cos squared space left parenthesis cos space theta right parenthesis plus sin squared space left parenthesis sin space theta right parenthesis$ is

As cos is a decreasing function and sin is an increasing function so the function

cos squared space left parenthesis cos space theta right parenthesis plus sin squared space left parenthesis sin space theta right parenthesis

is maximum when

theta

90 degree

.
So, the maximum value of

cos squared space left parenthesis cos space theta right parenthesis plus sin squared space left parenthesis sin space theta right parenthesis

cos squared space left parenthesis cos space 90 degree right parenthesis plus sin squared space left parenthesis sin space 90 degree right parenthesis equals cos squared 0 plus sin squared 1 equals 1 plus sin squared 1

For any real $theta$ , the maximum value of $cos squared space left parenthesis cos space theta right parenthesis plus sin squared space left parenthesis sin space theta right parenthesis$ is

As cos is a decreasing function and sin is an increasing function so the function

cos squared space left parenthesis cos space theta right parenthesis plus sin squared space left parenthesis sin space theta right parenthesis

is maximum when

theta

90 degree

.
So, the maximum value of

cos squared space left parenthesis cos space theta right parenthesis plus sin squared space left parenthesis sin space theta right parenthesis

cos squared space left parenthesis cos space 90 degree right parenthesis plus sin squared space left parenthesis sin space 90 degree right parenthesis equals cos squared 0 plus sin squared 1 equals 1 plus sin squared 1

Identify A and B

With H₂ / pd / CaCO₃ - is addition of ‘H’ know is oxidizing agent

Identify A and B

chemistry-General

With H₂ / pd / CaCO₃ - is addition of ‘H’ know is oxidizing agent

If $square root of 2 cos space A equals cos space B plus cos cubed space B text and end text square root of 2 sin text end text A equals sin space B minus sin cubed space B$ then sin (A-B) =

cos A = cos B + cos^{3} B..... equation 1

∴ cos A = 1/ \sqrt2 (cos B + cos^{3} B) ........ (Dividing both sides by \sqrt2)

√2 sin A = sin B - sin³ B..... equation 2

∴ sin A = 1/√2 (sin B - sin³ B) ........ (Dividing both sides by √2)
TO FIND-
Sin (A - B)
SOLUTION-
We know that-
Sin (A - B) = (Sin A * Cos B) - (Cos A * Sin B)
∴ Sin (A - B) = [1/√2 (sin B - sin³ B) * cos B] - [1/√2 (cos B + cos³ B) * sin B] ...... (From Equations i & ii)
∴ Sin (A - B) = [1/√2 * (sin B Cos B - sin³ B Cos B)] - [1/√2 * (sin B cos B + cos³ B * sin B)]
∴ Sin (A - B) = 1/√2 sin B Cos B - 1/√2 sin³ B Cos B - (1/√2 sin B cos B + 1/√2 cos³ B * sin B)
∴ Sin (A - B) = 1/√2 sin B Cos B - 1/√2 sin³ B Cos B - 1/√2 sin B cos B - 1/√2 cos³ B * sin B
∴ Sin (A - B) = 1/√2 sin B Cos B - 1/√2 sin³ B Cos B - 1/√2 sin B cos B - 1/√2 cos³ B * sin B
∴ Sin (A - B) = -1/√2 sin³ B Cos B - 1/√2 cos³ B * sin B

∴ Sin (A - B) = -1/√2 sin B Cos B (sin² B +cos² B)
= -1/2√2 sin2B
Now squaring and adding equation 1 and 2 we get

2 cos squared A plus 2 sin squared A equals cos squared B plus cos to the power of 6 B plus 2 cos to the power of 4 B plus sin squared B plus sin to the power of 6 B minus 2 sin to the power of 4 B rightwards double arrow 2 open parentheses cos squared A plus sin squared A close parentheses equals cos squared B plus sin squared B plus open parentheses cos squared B plus sin squared B close parentheses cubed minus 3 open parentheses cos squared B sin squared B close parentheses open parentheses cos squared B plus sin squared B close parentheses plus 2 open parentheses cos to the power of 4 B minus sin to the power of 4 B close parentheses rightwards double arrow 2 equals 1 plus 1 minus 3 over 4 sin squared 2 B plus 2 cos 2 B space space space space open square brackets 4 cos squared B sin squared B equals sin squared 2 B comma cos to the power of 4 B minus sin to the power of 4 B equals cos 2 B space close square brackets space space space open square brackets cos squared B plus sin squared B equals 1 close square brackets rightwards double arrow 0 equals negative 3 sin squared 2 B plus 8 cos 2 B rightwards double arrow 0 equals negative 3 open parentheses 1 minus cos squared 2 B close parentheses plus 8 cos 2 B space space space space open square brackets cos squared 2 B plus sin squared 2 B equals 1 close square brackets rightwards double arrow 0 equals 3 cos squared 2 B minus 3 plus 8 cos 2 B rightwards double arrow 3 cos squared 2 B plus 8 cos 2 B minus 3 equals 0 rightwards double arrow 3 cos squared 2 B plus 9 cos 2 B minus cos 2 B minus 3 equals 0 rightwards double arrow 3 cos 2 B open parentheses cos 2 B plus 3 close parentheses minus 1 open parentheses cos 2 B plus 3 close parentheses equals 0 rightwards double arrow open parentheses 3 cos 2 B minus 1 close parentheses open parentheses cos 2 B plus 3 close parentheses equals 0 rightwards double arrow cos 2 B equals 1 third space o r space cos 2 B equals negative 3 open parentheses n o t space p o s s i b l e close parentheses N o w comma space w e space k n o w space t h a t space open parentheses cos squared 2 B plus sin squared 2 B close parentheses equals 1 S o comma space 1 over 9 plus sin squared 2 B equals 1 rightwards double arrow sin squared 2 B equals 1 minus 1 over 9 equals 8 over 9 sin 2 B equals plus-or-minus fraction numerator 2 square root of 2 over denominator 3 end fraction t h e r e f o r e comma space sin open parentheses A minus B close parentheses equals fraction numerator negative sin 2 B over denominator 2 square root of 2 end fraction equals plus-or-minus fraction numerator 2 square root of 2 over denominator 3 end fraction cross times fraction numerator 1 over denominator 2 square root of 2 end fraction equals plus-or-minus 1 third

If $square root of 2 cos space A equals cos space B plus cos cubed space B text and end text square root of 2 sin text end text A equals sin space B minus sin cubed space B$ then sin (A-B) =

cos A = cos B + cos^{3} B..... equation 1

∴ cos A = 1/ \sqrt2 (cos B + cos^{3} B) ........ (Dividing both sides by \sqrt2)

√2 sin A = sin B - sin³ B..... equation 2

∴ sin A = 1/√2 (sin B - sin³ B) ........ (Dividing both sides by √2)
TO FIND-
Sin (A - B)
SOLUTION-
We know that-
Sin (A - B) = (Sin A * Cos B) - (Cos A * Sin B)
∴ Sin (A - B) = [1/√2 (sin B - sin³ B) * cos B] - [1/√2 (cos B + cos³ B) * sin B] ...... (From Equations i & ii)
∴ Sin (A - B) = [1/√2 * (sin B Cos B - sin³ B Cos B)] - [1/√2 * (sin B cos B + cos³ B * sin B)]
∴ Sin (A - B) = 1/√2 sin B Cos B - 1/√2 sin³ B Cos B - (1/√2 sin B cos B + 1/√2 cos³ B * sin B)
∴ Sin (A - B) = 1/√2 sin B Cos B - 1/√2 sin³ B Cos B - 1/√2 sin B cos B - 1/√2 cos³ B * sin B
∴ Sin (A - B) = 1/√2 sin B Cos B - 1/√2 sin³ B Cos B - 1/√2 sin B cos B - 1/√2 cos³ B * sin B
∴ Sin (A - B) = -1/√2 sin³ B Cos B - 1/√2 cos³ B * sin B

∴ Sin (A - B) = -1/√2 sin B Cos B (sin² B +cos² B)
= -1/2√2 sin2B
Now squaring and adding equation 1 and 2 we get

2 cos squared A plus 2 sin squared A equals cos squared B plus cos to the power of 6 B plus 2 cos to the power of 4 B plus sin squared B plus sin to the power of 6 B minus 2 sin to the power of 4 B rightwards double arrow 2 open parentheses cos squared A plus sin squared A close parentheses equals cos squared B plus sin squared B plus open parentheses cos squared B plus sin squared B close parentheses cubed minus 3 open parentheses cos squared B sin squared B close parentheses open parentheses cos squared B plus sin squared B close parentheses plus 2 open parentheses cos to the power of 4 B minus sin to the power of 4 B close parentheses rightwards double arrow 2 equals 1 plus 1 minus 3 over 4 sin squared 2 B plus 2 cos 2 B space space space space open square brackets 4 cos squared B sin squared B equals sin squared 2 B comma cos to the power of 4 B minus sin to the power of 4 B equals cos 2 B space close square brackets space space space open square brackets cos squared B plus sin squared B equals 1 close square brackets rightwards double arrow 0 equals negative 3 sin squared 2 B plus 8 cos 2 B rightwards double arrow 0 equals negative 3 open parentheses 1 minus cos squared 2 B close parentheses plus 8 cos 2 B space space space space open square brackets cos squared 2 B plus sin squared 2 B equals 1 close square brackets rightwards double arrow 0 equals 3 cos squared 2 B minus 3 plus 8 cos 2 B rightwards double arrow 3 cos squared 2 B plus 8 cos 2 B minus 3 equals 0 rightwards double arrow 3 cos squared 2 B plus 9 cos 2 B minus cos 2 B minus 3 equals 0 rightwards double arrow 3 cos 2 B open parentheses cos 2 B plus 3 close parentheses minus 1 open parentheses cos 2 B plus 3 close parentheses equals 0 rightwards double arrow open parentheses 3 cos 2 B minus 1 close parentheses open parentheses cos 2 B plus 3 close parentheses equals 0 rightwards double arrow cos 2 B equals 1 third space o r space cos 2 B equals negative 3 open parentheses n o t space p o s s i b l e close parentheses N o w comma space w e space k n o w space t h a t space open parentheses cos squared 2 B plus sin squared 2 B close parentheses equals 1 S o comma space 1 over 9 plus sin squared 2 B equals 1 rightwards double arrow sin squared 2 B equals 1 minus 1 over 9 equals 8 over 9 sin 2 B equals plus-or-minus fraction numerator 2 square root of 2 over denominator 3 end fraction t h e r e f o r e comma space sin open parentheses A minus B close parentheses equals fraction numerator negative sin 2 B over denominator 2 square root of 2 end fraction equals plus-or-minus fraction numerator 2 square root of 2 over denominator 3 end fraction cross times fraction numerator 1 over denominator 2 square root of 2 end fraction equals plus-or-minus 1 third

parallel

Observer the following reactions and predict the nature of A and B

Observer the following reactions and predict the nature of A and B

chemistry-General

on ozonolysis gives

on ozonolysis gives

chemistry-General

Which of the following reactions will yield 2, 2-dibromopropane?

Which of the following reactions will yield 2, 2-dibromopropane?

chemistry-General

parallel

If $fraction numerator cos space x over denominator a end fraction equals fraction numerator cos begin display style space end style left parenthesis x plus theta right parenthesis over denominator b end fraction equals fraction numerator cos begin display style space end style left parenthesis x plus 2 theta right parenthesis over denominator c end fraction equals fraction numerator cos begin display style space end style left parenthesis x plus 3 theta right parenthesis over denominator d end fraction$ then $fraction numerator a plus c over denominator b plus d end fraction$ is equal to

If $fraction numerator cos space x over denominator a end fraction equals fraction numerator cos begin display style space end style left parenthesis x plus theta right parenthesis over denominator b end fraction equals fraction numerator cos begin display style space end style left parenthesis x plus 2 theta right parenthesis over denominator c end fraction equals fraction numerator cos begin display style space end style left parenthesis x plus 3 theta right parenthesis over denominator d end fraction$ then $fraction numerator a plus c over denominator b plus d end fraction$ is equal to

If $tan space alpha equals P over q$ where $alpha equals 2 beta comma alpha$ being an acute angle then $1 half$ $left square bracket p cosec space 2 beta plus q sec space 2 beta right square bracket$ is equal to

If $tan space alpha equals P over q$ where $alpha equals 2 beta comma alpha$ being an acute angle then $1 half$ $left square bracket p cosec space 2 beta plus q sec space 2 beta right square bracket$ is equal to

Let A,B,C be three angles such that $A equals pi over 4$ and $tan space B tan space C equals p$ . Then, all possible values of P such that A,B,C are the angles of a triangle is

Let A,B,C be three angles such that $A equals pi over 4$ and $tan space B tan space C equals p$ . Then, all possible values of P such that A,B,C are the angles of a triangle is

parallel

is an example for

is an example for

chemistry-General

If $y equals left parenthesis 1 plus tan space A right parenthesis left parenthesis 1 minus tan space B right parenthesis$ where $A minus B equals pi over 4$ then $left parenthesis y plus 1 right parenthesis to the power of y plus 1 end exponent$ =

If $y equals left parenthesis 1 plus tan space A right parenthesis left parenthesis 1 minus tan space B right parenthesis$ where $A minus B equals pi over 4$ then $left parenthesis y plus 1 right parenthesis to the power of y plus 1 end exponent$ =

What is the hybridization state of benzyl carbonium ion

All carbons are sp²

What is the hybridization state of benzyl carbonium ion

chemistry-General

All carbons are sp²

parallel

An integral value of a for which there is a solution of the equation $a cos space x plus cot space x 1 equals cosec space x$ is $left parenthesis sin space 2 x not equal to 0 right parenthesis$

An integral value of a for which there is a solution of the equation $a cos space x plus cot space x 1 equals cosec space x$ is $left parenthesis sin space 2 x not equal to 0 right parenthesis$

If $sin space x plus cosec space x plus tan space y plus cot space y equals 4$ where x and y $element of open parentheses 0 comma pi over 2 close parentheses tan space y over 2$ s a root of the equation

If $sin space x plus cosec space x plus tan space y plus cot space y equals 4$ where x and y $element of open parentheses 0 comma pi over 2 close parentheses tan space y over 2$ s a root of the equation

The direction of the water flow in given cells X,Y $&$ Z can be presented as :

The direction of the water flow in given cells X,Y $&$ Z can be presented as :

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.