Question

Guys, Please answer this question, with full explanation.​

Answer 1

Hope you get the right answer
Hence proved ,

Answer 2

Question

to prove :

$\frac{ \sin {}^{4} (x) + \cos{}^{4} (x)}{1 - 2 \sin {}^{2} (x) \cos {}^{2} (x) } = 1$

solution

RHS

$= \frac{ \sin {}^{4} (x) + \cos {}^{4} (x) }{1 - 2 \sin {}^{2} (x) \cos {}^{2} (x) }$

$= \frac{ \cos {}^{4} (x) + \sin {}^{4} (x) }{1 - 2(1 - \cos {}^{2} (x) ) \cos {}^{2} (x) }$

$= \frac{ \sin {}^{4} (x) + \cos {}^{4} (x) }{ \sin {}^{2} (x) + \cos {}^{2} (x) - 2( \cos {}^{2} ( x ) - \cos {}^{4} (x) )}$

$= \frac{ \sin {}^{4} (x) + \cos {}^{4} (x) }{ \cos {}^{4} (x) + \cos {}^{4} (x) + \sin {}^{2} (x) + \cos {}^{2} (x) - 2 \cos {}^{2} (x) }$

$= \frac{ \sin {}^{4} (x) + \cos {}^{4} (x) }{ \cos { }^{4} (x) + \sin {}^{2} (x) - \cos {}^{2} (x) + (1 - \sin {}^{2} (x)) {}^{2} }$

on solving denominator you get ;

$= \frac{ \sin {}^{4} (x) + \cos {}^{4} (x) }{ \cos {}^{4} (x) + \sin {}^{4} (x) }$

$= 1$

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