Question

This one is of trigonometry please answer step by step with a attachment

Answer 1

Question :-

Prove that

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

Solution :

Take LHS

$\cos {}^{4} (x) - \sin {}^{4} (x)$

We know that :-

$a {}^{4} - b {}^{4} = ( {a}^{2} - {b}^{2} )( {a}^{2} + {b}^{2} )$

Hence,

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

As,

$\cos {}^{2} x + \sin {}^{2} x = 1$

So,

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

LHS = RHS - -(PROVED)

Answer 2

Answer:

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