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 $alpha comma beta comma gamma text are acute angles and end text cos text end text theta equals sin space beta divided by sin space alpha comma cos space ϕ equals sin space gamma divided by sin invisible function application alpha$ and $cos space left parenthesis theta minus ϕ right parenthesis equals sin space beta sin space gamma$ then the value of $tan squared space alpha minus tan squared space beta minus tan squared space gamma$ is equal to

-1
0
1
2

hint Hint:

In this question, we have to find the value of $tan squared space alpha minus tan squared space beta minus tan squared space gamma$ . For that first we will use the given equation to find the value of one of the three term, then we can put the value obtained in $tan squared space alpha minus tan squared space beta minus tan squared space gamma$ to find the required answer.

The correct answer is: 0

$cos space left parenthesis theta minus ϕ right parenthesis equals sin space beta sin space gamma rightwards double arrow open parentheses cos space theta. cos space ϕ minus sin space theta. sin space ϕ close parentheses equals sin space beta. sin space gamma rightwards double arrow open parentheses cos space theta. cos space ϕ minus sin space beta sin space gamma close parentheses equals sin space theta. sin space ϕ S q u a r i n g space b o t h space s i d e s comma space w e space g e t colon rightwards double arrow open parentheses cos space theta. cos space ϕ minus sin space beta sin space gamma close parentheses squared equals sin squared theta sin squared ϕ rightwards double arrow open parentheses fraction numerator sin beta over denominator sin alpha end fraction fraction numerator sin gamma over denominator sin alpha end fraction minus sin beta. sin gamma close parentheses squared equals open parentheses 1 minus cos squared theta close parentheses open parentheses 1 minus cos squared ϕ close parentheses rightwards double arrow fraction numerator sin squared beta sin squared gamma open parentheses 1 minus sin squared alpha close parentheses over denominator sin squared alpha end fraction equals open parentheses 1 minus fraction numerator sin squared beta over denominator sin squared alpha end fraction close parentheses open parentheses 1 minus fraction numerator sin squared gamma over denominator sin squared alpha end fraction close parentheses rightwards double arrow sin squared beta sin squared gamma open parentheses 1 plus sin to the power of 4 alpha minus 2 sin squared alpha close parentheses equals open parentheses sin squared alpha minus sin squared beta close parentheses open parentheses sin squared alpha minus sin squared gamma close parentheses rightwards double arrow sin squared beta sin squared gamma plus sin squared beta sin squared gamma sin to the power of 4 alpha minus 2 sin squared alpha sin squared beta sin squared gamma equals sin to the power of 4 alpha minus sin squared alpha sin squared beta minus sin squared alpha sin squared gamma plus sin squared beta sin squared gamma rightwards double arrow sin to the power of 4 alpha open parentheses 1 minus sin squared beta sin squared gamma close parentheses minus sin squared gamma open parentheses sin squared beta plus sin squared gamma minus 2 sin squared beta sin squared gamma close parentheses equals 0 rightwards double arrow sin to the power of 4 alpha open parentheses 1 minus sin squared beta sin squared gamma close parentheses equals sin squared gamma open parentheses sin squared beta plus sin squared gamma minus 2 sin squared beta sin squared gamma close parentheses rightwards double arrow sin squared alpha equals fraction numerator sin squared beta plus sin squared gamma minus 2 sin squared beta sin squared gamma over denominator 1 minus sin squared beta sin squared gamma end fraction...... e q u a t i o n space 1 rightwards double arrow cos squared alpha equals 1 minus fraction numerator sin squared beta plus sin squared gamma minus 2 sin squared beta sin squared gamma over denominator 1 minus sin squared beta sin squared gamma end fraction rightwards double arrow cos squared alpha equals fraction numerator 1 minus sin squared beta minus sin squared gamma plus sin squared beta sin squared gamma over denominator 1 minus sin squared beta sin squared gamma end fraction..... e q u a t i o n space 2 f r o m space 1 space a n d space 2 tan squared alpha equals fraction numerator sin squared beta plus sin squared gamma minus 2 sin squared beta sin squared gamma over denominator 1 minus sin squared beta minus sin squared gamma plus s in squared beta sin squared gamma end fraction equals fraction numerator sin squared beta minus sin squared beta sin squared gamma plus sin squared gamma minus sin squared beta sin squared gamma over denominator open parentheses 1 minus sin squared beta close parentheses minus sin squared gamma open parentheses 1 minus sin squared beta close parentheses end fraction equals fraction numerator sin squared beta open parentheses 1 minus sin squared gamma close parentheses plus sin squared gamma open parentheses 1 minus sin squared beta close parentheses over denominator open parentheses 1 minus sin squared beta close parentheses open parentheses 1 minus sin squared gamma close parentheses end fraction equals fraction numerator sin squared beta cos squared gamma plus sin squared gamma cos squared beta over denominator cos squared beta cos squared gamma end fraction N o w comma space tan squared alpha minus tan squared beta minus tan squared gamma equals fraction numerator sin squared beta cos squared gamma plus sin squared gamma cos squared beta over denominator cos squared beta cos squared gamma end fraction minus fraction numerator sin squared beta over denominator cos squared beta end fraction minus fraction numerator sin squared gamma over denominator cos squared gamma end fraction equals fraction numerator sin squared beta cos squared gamma plus sin squared gamma cos squared beta minus sin squared beta cos squared gamma minus sin squared gamma cos squared beta over denominator cos squared beta cos squared gamma end fraction equals 0$

Related Questions to study

If $x sin space a plus y sin space 2 a plus z sin space 3 a equals sin space 4 a x sin space b plus y sin space 2 b plus z sin space 3 b equals sin space 4 b comma x sin space c plus y sin space 2 c plus z sin space 3 c equals sin space 4 c$ Then the roots of the equation $t cubed minus open parentheses z over 2 close parentheses t squared minus open parentheses fraction numerator y plus z over denominator 4 end fraction close parentheses t plus open parentheses fraction numerator z minus x over denominator 8 end fraction close parentheses equals 0 comma a comma b comma c not equal to n pi$ are

If $x sin space a plus y sin space 2 a plus z sin space 3 a equals sin space 4 a x sin space b plus y sin space 2 b plus z sin space 3 b equals sin space 4 b comma x sin space c plus y sin space 2 c plus z sin space 3 c equals sin space 4 c$ Then the roots of the equation $t cubed minus open parentheses z over 2 close parentheses t squared minus open parentheses fraction numerator y plus z over denominator 4 end fraction close parentheses t plus open parentheses fraction numerator z minus x over denominator 8 end fraction close parentheses equals 0 comma a comma b comma c not equal to n pi$ are

If $equals fraction numerator 2 pi over denominator 7 end fraction$ ,then tan $alpha tan invisible function application 2 alpha plus tan invisible function application 2 alpha tan invisible function application 4 alpha plus tan invisible function application 4 alpha tan invisible function application alpha equals$

If $equals fraction numerator 2 pi over denominator 7 end fraction$ ,then tan $alpha tan invisible function application 2 alpha plus tan invisible function application 2 alpha tan invisible function application 4 alpha plus tan invisible function application 4 alpha tan invisible function application alpha equals$

If the mapping $f left parenthesis x right parenthesis equals a x plus b comma a less than 0$ maps [-1,1] onto [0,2] then for all values of $theta$ , $A equals cos squared space theta plus sin to the power of 4 space theta$ is such that

If the mapping $f left parenthesis x right parenthesis equals a x plus b comma a less than 0$ maps [-1,1] onto [0,2] then for all values of $theta$ , $A equals cos squared space theta plus sin to the power of 4 space theta$ is such that

parallel

If $fraction numerator sec to the power of 8 space theta over denominator a end fraction plus fraction numerator tan to the power of 8 begin display style space end style theta over denominator b end fraction equals fraction numerator 1 over denominator a plus b end fraction$ then

If $fraction numerator sec to the power of 8 space theta over denominator a end fraction plus fraction numerator tan to the power of 8 begin display style space end style theta over denominator b end fraction equals fraction numerator 1 over denominator a plus b end fraction$ then

The sum of the series, $sin space theta sec space 3 theta plus sin space 3 theta sec space 3 squared theta plus sin space 3 squared theta sec space 3 cubed theta plus times times$ upto n terms, is

The sum of the series, $sin space theta sec space 3 theta plus sin space 3 theta sec space 3 squared theta plus sin space 3 squared theta sec space 3 cubed theta plus times times$ upto n terms, is

In a triangle $ABC$

In a triangle $ABC$

parallel

The value of $sum from n equals 1 to straight infinity of fraction numerator tan begin display style space end style open parentheses theta over 2 to the power of n close parentheses over denominator 2 to the power of n minus 1 end exponent cos space theta over 2 to the power of n minus 1 end exponent end fraction$ is

The value of $sum from n equals 1 to straight infinity of fraction numerator tan begin display style space end style open parentheses theta over 2 to the power of n close parentheses over denominator 2 to the power of n minus 1 end exponent cos space theta over 2 to the power of n minus 1 end exponent end fraction$ is

If the equation $cot to the power of 4 space x minus 2 cos space e c squared x plus a squared$ =0 has at least one solution, then the sum of all possible integral values of 'a' is equal to

If the equation $cot to the power of 4 space x minus 2 cos space e c squared x plus a squared$ =0 has at least one solution, then the sum of all possible integral values of 'a' is equal to

$cos to the power of 6 space pi over 16 plus cos to the power of 6 space fraction numerator 3 pi over denominator 16 end fraction plus cos to the power of 6 space fraction numerator 5 pi over denominator 16 end fraction plus cos to the power of 6 space fraction numerator 7 pi over denominator 16 end fraction$ =

$cos to the power of 6 space pi over 16 plus cos to the power of 6 space fraction numerator 3 pi over denominator 16 end fraction plus cos to the power of 6 space fraction numerator 5 pi over denominator 16 end fraction plus cos to the power of 6 space fraction numerator 7 pi over denominator 16 end fraction$ =

parallel

If $a sin space x plus b cos space left parenthesis x plus theta right parenthesis plus b cos space left parenthesis x minus theta right parenthesis equals$ d then the minimum value of $vertical line cos space theta vertical line$ is equal to (where is variable)

If $a sin space x plus b cos space left parenthesis x plus theta right parenthesis plus b cos space left parenthesis x minus theta right parenthesis equals$ d then the minimum value of $vertical line cos space theta vertical line$ is equal to (where is variable)

$a squared plus b squared plus 2 a b cos space theta equals 1 comma c squared plus d squared plus 2 c d cos space theta equals 1$ and $a c plus b d plus left parenthesis a d plus b c right parenthesis cos space theta equals 0$ then $a squared plus c squared$ =

$a squared plus b squared plus 2 a b cos space theta equals 1 comma c squared plus d squared plus 2 c d cos space theta equals 1$ and $a c plus b d plus left parenthesis a d plus b c right parenthesis cos space theta equals 0$ then $a squared plus c squared$ =

$sin to the power of 4 space pi over 16 plus sin to the power of 4 fraction numerator 3 pi over denominator 16 end fraction plus sin to the power of 4 space fraction numerator 5 pi over denominator 16 end fraction plus sin to the power of 4 space fraction numerator 7 pi over denominator 16 end fraction$

$sin to the power of 4 space pi over 16 plus sin to the power of 4 fraction numerator 3 pi over denominator 16 end fraction plus sin to the power of 4 space fraction numerator 5 pi over denominator 16 end fraction plus sin to the power of 4 space fraction numerator 7 pi over denominator 16 end fraction$

parallel

If $cos space left parenthesis A plus B plus C right parenthesis equals cos space A cos space B cos space C comma$ then $fraction numerator 8 sin space left parenthesis B plus C right parenthesis sin space left parenthesis C plus A right parenthesis sin space left parenthesis A plus B right parenthesis over denominator sin space 2 A sin space 2 B sin space 2 C end fraction$ =

If $cos space left parenthesis A plus B plus C right parenthesis equals cos space A cos space B cos space C comma$ then $fraction numerator 8 sin space left parenthesis B plus C right parenthesis sin space left parenthesis C plus A right parenthesis sin space left parenthesis A plus B right parenthesis over denominator sin space 2 A sin space 2 B sin space 2 C end fraction$ =

The maximum value of the expression $open vertical bar square root of open parentheses sin squared space x plus 2 a squared close parentheses end root minus square root of open parentheses 2 a squared minus 1 minus cos squared space x close parentheses end root close vertical bar$
where $a$ and x are real numbers is

The maximum value of the expression $open vertical bar square root of open parentheses sin squared space x plus 2 a squared close parentheses end root minus square root of open parentheses 2 a squared minus 1 minus cos squared space x close parentheses end root close vertical bar$
where $a$ and x are real numbers is

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

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

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.