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

If $tan space theta minus cot space theta equals a$ and $cos space theta minus sin space theta equals b$ then $open parentheses a squared plus 4 close parentheses open parentheses b squared minus 1 close parentheses squared$

1
3
4
5

hint Hint:

In the question we will simplify the given equations using some trigonometric identities.

The correct answer is: 4

$tan space theta minus cot space theta equals a rightwards double arrow fraction numerator sin theta over denominator cos theta end fraction minus fraction numerator cos theta over denominator sin theta end fraction equals a space space space space space space space rightwards double arrow fraction numerator sin squared theta minus cos squared theta over denominator cos theta sin theta end fraction equals a rightwards double arrow fraction numerator negative 2 cos 2 theta over denominator sin 2 theta end fraction equals a space space space space space space space space space open square brackets cos squared x minus sin squared x equals cos 2 x comma space 2 sin x space cos x space equals 2 sin 2 x close square brackets s q u a r i n g space b o t h space s i d e s comma rightwards double arrow fraction numerator 4 cos squared 2 theta over denominator sin squared 2 theta end fraction equals a squared a d d i n g space 4 space o n space b o t h space s i d e s comma rightwards double arrow fraction numerator 4 cos squared 2 theta over denominator sin squared 2 theta end fraction plus 4 equals a squared plus 4 rightwards double arrow fraction numerator 4 cos squared 2 theta plus 4 sin squared 2 theta over denominator sin squared 2 theta end fraction equals a squared plus 4 rightwards double arrow fraction numerator 4 over denominator sin squared 2 theta end fraction equals a squared plus 4........ e q u a t i o n space 1 space space space space space space space space space space space space space space open square brackets cos squared x plus sin squared x equals 1 close square brackets$
$cos space theta space minus sin theta space equals b s q u a r i n g space b o t h space s i d e s comma space rightwards double arrow open parentheses cos theta minus sin theta close parentheses squared equals b squared rightwards double arrow cos squared theta plus sin squared theta minus 2 sin theta cos theta equals b squared rightwards double arrow 1 minus sin 2 theta equals b squared space space space space space space open square brackets cos squared theta plus sin squared theta equals 1 comma space 2 sin theta cos theta equals sin 2 theta close square brackets rightwards double arrow negative sin 2 theta equals b squared minus 1 s q u a r i n g space b o t h space s i d e s comma rightwards double arrow sin squared 2 theta equals open parentheses b squared minus 1 close parentheses squared......... e q u a t i o n space 2$
on multiplying equation 1 and 2,
$open parentheses a squared plus 4 close parentheses open parentheses b squared minus 1 close parentheses squared equals fraction numerator 4 over denominator sin squared 2 theta end fraction cross times sin squared 2 theta equals 4$

Related Questions to study

The maximum value of $open parentheses cos space alpha subscript 1 close parentheses open parentheses cos space alpha subscript 2 close parentheses horizontal ellipsis open parentheses cos space alpha subscript n close parentheses$ under the restrictions $0 less or equal than alpha subscript 1 comma alpha subscript 2 horizontal ellipsis horizontal ellipsis alpha subscript n less or equal than pi over 2$ and $cot space alpha subscript 1 times cot space alpha subscript 2 horizontal ellipsis horizontal ellipsis cot space alpha subscript n equals 1$ is

The maximum value of $open parentheses cos space alpha subscript 1 close parentheses open parentheses cos space alpha subscript 2 close parentheses horizontal ellipsis open parentheses cos space alpha subscript n close parentheses$ under the restrictions $0 less or equal than alpha subscript 1 comma alpha subscript 2 horizontal ellipsis horizontal ellipsis alpha subscript n less or equal than pi over 2$ and $cot space alpha subscript 1 times cot space alpha subscript 2 horizontal ellipsis horizontal ellipsis cot space alpha subscript n equals 1$ is

Let $P equals left curly bracket theta colon sin space theta minus cos space theta equals square root of 2 cos space theta right curly bracket text and end text Q equals left curly bracket theta colon sin space theta plus cos space theta equals square root of 2 sin space theta right curly bracket$ be two sets. Then

Let $P equals left curly bracket theta colon sin space theta minus cos space theta equals square root of 2 cos space theta right curly bracket text and end text Q equals left curly bracket theta colon sin space theta plus cos space theta equals square root of 2 sin space theta right curly bracket$ be two sets. Then

If $0 less than alpha less than pi over 6$ then $alpha left parenthesis cosec space alpha right parenthesis$ is

If $0 less than alpha less than pi over 6$ then $alpha left parenthesis cosec space alpha right parenthesis$ is

parallel

A long cylindrical tube carries a highly polished piston and has a side opening. A tuning fork of frequency n is sounded at the sound heard by the listener charges if the piston is moves in or out. At a particular position of the piston is moved through a distance of 9 cm, the intensity of sound becomes minimum, if the speed of sound is 360 m/s, the value of n is

A long cylindrical tube carries a highly polished piston and has a side opening. A tuning fork of frequency n is sounded at the sound heard by the listener charges if the piston is moves in or out. At a particular position of the piston is moved through a distance of 9 cm, the intensity of sound becomes minimum, if the speed of sound is 360 m/s, the value of n is

physics-General

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

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

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

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

parallel

Identify A and B

Identify A and B

chemistry-General

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) =

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) =

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

parallel

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

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

parallel

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

is an example for

is an example for

chemistry-General

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.