Question

cos power4 theta - sin power 4 theta = cos 2 theta
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Answer 1

Step-by-step explanation:

${cos}^{4} \theta - {sin}^{4} \theta = {cos}2 \theta$

$LHS = {cos}^{4} \theta - {sin}^{4} \theta$

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

$\scriptsize = ({cos}^{2} \theta - {sin}^{2} \theta )({cos}^{2} \theta + {sin}^{2} \theta ) \: ( \because {a}^{2} - {b}^{2} = (a - b)(a + b))$

$= cos2 \theta.1 \: \: \: \: ( \because{sin}^{2} \theta + {cos}^{2} \theta=1)$

$= cos2 \theta$

= RHS

Hence proved