Question

Cos raise to 4 x - sin raise to 4 x is equal tocos 2x

Answer 1

Step-by-step explanation:

${cos}^{2} x + {sin}^{2} x = 1 \\ \\ cos(x + y) = cosx \: cosy - sinx \: siny \\ \\ {x}^{2} - {y}^{2} = (x + y)(x - y) \\ \\ now \\ \\ {cos}^{4} x - {sin}^{4} x \\ \\ = {( {cos}^{2}x) }^{2} - {( {sin}^{2} x)}^{2} \\ \\ = ( {cos}^{2} x - {sin}^{2} x) ( {cos}^{2} x + {sin}^{2} x) \\ \\ = ( {cos}^{2} x - {sin}^{2} x) \\ \\ = (cosx \: cosx) - (sinx \: sinx) \\ \\ = cos(x + x) \\ \\ = cos2x$

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