Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

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 $fraction numerator sin to the power of 4 space theta over denominator a end fraction plus fraction numerator cos to the power of 4 begin display style space end style theta over denominator b end fraction equals fraction numerator 1 over denominator a plus b end fraction text then end text fraction numerator sin to the power of 8 begin display style text end text end style theta over denominator a cubed end fraction plus fraction numerator cos to the power of 8 begin display style space end style theta over denominator b cubed end fraction equals$

$\frac{1}{(a + b)^{3}}$
$\frac{1}{(a + b)^{2}}$
$a + b$
$\frac{1}{a + b}$

hint Hint:

In this question, we have to find the value of $fraction numerator sin to the power of 8 begin display style text end text end style theta over denominator a cubed end fraction plus fraction numerator cos to the power of 8 begin display style space end style theta over denominator b cubed end fraction$ , if it is given that $fraction numerator sin to the power of 4 space theta over denominator a end fraction plus fraction numerator cos to the power of 4 begin display style space end style theta over denominator b end fraction equals fraction numerator 1 over denominator a plus b end fraction$ . First we will find the value of any trigonometric function using the given equation, for this question we will find the value of either sine or cosine function. Later we will substitute the value of the derived function to find the other required function and later solve it to get the value of required function.

The correct answer is: $fraction numerator 1 over denominator left parenthesis a plus b right parenthesis cubed end fraction$

$fraction numerator sin to the power of 4 space theta over denominator a end fraction plus fraction numerator cos to the power of 4 begin display style space end style theta over denominator b end fraction equals fraction numerator 1 over denominator a plus b end fraction rightwards double arrow fraction numerator b sin to the power of 4 theta plus a open parentheses 1 minus sin squared theta close parentheses squared over denominator a b end fraction equals fraction numerator 1 over denominator a plus b end fraction space rightwards double arrow fraction numerator b sin to the power of 4 theta plus a plus a sin to the power of 4 theta minus 2 a sin squared theta over denominator a b end fraction equals fraction numerator 1 over denominator a plus b end fraction rightwards double arrow open parentheses a plus b close parentheses sin to the power of 4 theta minus 2 a space sin squared theta equals fraction numerator a b over denominator a plus b end fraction minus a rightwards double arrow open parentheses a plus b close parentheses sin to the power of 4 theta minus 2 a space sin squared theta equals fraction numerator a b minus a squared minus a b over denominator a plus b end fraction rightwards double arrow open parentheses a plus b close parentheses sin to the power of 4 theta minus 2 a space sin squared theta equals fraction numerator negative a squared over denominator a plus b end fraction rightwards double arrow open parentheses a plus b close parentheses squared sin to the power of 4 theta minus 2 a left parenthesis a plus b right parenthesis space sin squared theta plus a squared equals 0 rightwards double arrow open parentheses left parenthesis a plus b right parenthesis sin squared theta minus a close parentheses squared equals 0 rightwards double arrow left parenthesis a plus b right parenthesis sin squared theta minus a equals 0 rightwards double arrow sin squared theta equals fraction numerator a over denominator a plus b end fraction N o w comma space fraction numerator sin to the power of 8 space theta over denominator a cubed end fraction plus fraction numerator cos to the power of 8 begin display style space end style theta over denominator b cubed end fraction equals fraction numerator begin display style a to the power of 4 over open parentheses a plus b close parentheses to the power of 4 end style over denominator a cubed end fraction plus fraction numerator open parentheses 1 minus a to the power of 4 over open parentheses a plus b close parentheses to the power of 4 close parentheses over denominator b cubed end fraction equals fraction numerator begin display style a to the power of 4 over open parentheses a plus b close parentheses to the power of 4 end style over denominator a cubed end fraction plus fraction numerator begin display style b to the power of 4 over open parentheses a plus b close parentheses to the power of 4 end style over denominator b cubed end fraction equals a over left parenthesis a plus b right parenthesis to the power of 4 plus b over left parenthesis a plus b right parenthesis to the power of 4 equals fraction numerator a plus b over denominator left parenthesis a plus b right parenthesis to the power of 4 end fraction equals 1 over left parenthesis a plus b right parenthesis cubed$

Related Questions to study

$0 less or equal than a less or equal than 3 comma 0 less or equal than b less or equal than 3$ and the equation $x squared plus 4 plus 3 cos space left parenthesis a x plus b right parenthesis equals 2 x$ has at least one solution then the value of (a+b)

$0 less or equal than a less or equal than 3 comma 0 less or equal than b less or equal than 3$ and the equation $x squared plus 4 plus 3 cos space left parenthesis a x plus b right parenthesis equals 2 x$ has at least one solution then the value of (a+b)

Correct order for stability of carbocation is

Correct order for stability of carbocation is

ChemistryGeneral

If $x equals sec space theta plus tan space theta comma y equals cosec space theta minus cot space theta text then end text y equals$

If $x equals sec space theta plus tan space theta comma y equals cosec space theta minus cot space theta text then end text y equals$

parallel

For all values of $theta$ , the values of $3 minus cos space theta plus cos space open parentheses theta plus pi over 3 close parentheses$ lie in the interval

For all values of $theta$ , the values of $3 minus cos space theta plus cos space open parentheses theta plus pi over 3 close parentheses$ lie in the interval

$left parenthesis sin space x minus cos space x right parenthesis squared plus cos squared space open parentheses pi over 4 minus x close parentheses element of$

$left parenthesis sin space x minus cos space x right parenthesis squared plus cos squared space open parentheses pi over 4 minus x close parentheses element of$

$5 cos space theta plus 3 cos space open parentheses theta minus pi over 3 close parentheses plus 8 element of$

$5 cos space theta plus 3 cos space open parentheses theta minus pi over 3 close parentheses plus 8 element of$

parallel

$cos space open parentheses x plus pi over 6 close parentheses cos space open parentheses x minus pi over 6 close parentheses element of$

$cos space open parentheses x plus pi over 6 close parentheses cos space open parentheses x minus pi over 6 close parentheses element of$

does not exist Extreme Values; $cos space invisible function application x plus sin to the power of 4 space x element of$

does not exist Extreme Values; $cos space invisible function application x plus sin to the power of 4 space x element of$

$left parenthesis sin space x plus cos space x right parenthesis squared plus cos squared space open parentheses pi over 4 plus x close parentheses element of$

$left parenthesis sin space x plus cos space x right parenthesis squared plus cos squared space open parentheses pi over 4 plus x close parentheses element of$

parallel

The minimum and maximum values of $cos space x plus 3 square root of 2 sin space open parentheses x plus pi over 4 close parentheses plus 6$ are

The minimum and maximum values of $cos space x plus 3 square root of 2 sin space open parentheses x plus pi over 4 close parentheses plus 6$ are

The minimum and maximum values of $sin space open parentheses x plus pi over 4 close parentheses sin space open parentheses x minus pi over 4 close parentheses$ are

The minimum and maximum values of $sin space open parentheses x plus pi over 4 close parentheses sin space open parentheses x minus pi over 4 close parentheses$ are

$sin squared space x plus cos to the power of 4 space x element of$

$sin squared space x plus cos to the power of 4 space x element of$

parallel

A piston fitted in cylindrical pipe is pulled as shown in the figure. A tuning fork is sounded at open end and loudest sound is heard at open length 13cm, 41 cm and 69 cm, the frequency of tuning fork if velocity of sound is $350 m s to the power of negative 1 end exponent$ is

A piston fitted in cylindrical pipe is pulled as shown in the figure. A tuning fork is sounded at open end and loudest sound is heard at open length 13cm, 41 cm and 69 cm, the frequency of tuning fork if velocity of sound is $350 m s to the power of negative 1 end exponent$ is

physics-General

In a sine wave, position of different particles at time $t equals 0$ is shown in figure. The equation for this wave travelling along positive $x minus a x i s$ can be

In a sine wave, position of different particles at time $t equals 0$ is shown in figure. The equation for this wave travelling along positive $x minus a x i s$ can be

physics-General

The function $sin space open parentheses x squared close parentheses$ $plus cos space square root of x$ is

The function $sin space open parentheses x squared close parentheses$ $plus cos space square root of x$ is

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.