Question

if x sin cube theta + Y cos cube theta equal to sin theta cos theta and x sin theta = Y cos theta prove that x squared plus y squared equals to 1

Answer 1

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Answer 2

Answer:

We have ,

$xsin^{3}\theta+ycos^{3}\theta=sin\theta cos\theta$

$\implies xsin\theta (sin^{2}\theta)+ (y cos\theta) cos^{2}\theta = sin\theta cos\theta$

$\implies xsin\theta (sin^{2}\theta)+ (x sin\theta) cos^{2}\theta = sin\theta cos\theta$

$Since, xsin\theta = y cos\theta$

$xsin\theta(sin^{2}\theta+cos^{2}\theta) = sin\theta cos \theta$

$\implies xsin\theta = sin\theta cos\theta$

$\implies x = cos\theta$

$Now ,xsin\theta = ycos\theta \:(given)$

$\implies cos\theta sin\theta = ycos\theta \:(Since,x=cos\theta)$

$\implies y = sin\theta$

$Hence, \\x^{2}+y^{2}=cos^{2}\theta+ sin^{2}\theta =1$

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