Question

show that cos2∅=cos∧4(∅)-sin∧4(∅)

Answer 1

$cos2\alpha=cos^4\alpha-sin^4\alpha$

$RHS$

$\boxed{(cos^2\alpha-sin^2\alpha)(cos^2\alpha+sin^2\alpha )}$

$\boxed{cos^2\alpha+sin^2\alpha=1 }$

$\boxed{cos^2\alpha-sin^2\alpha=cos2\alpha }$

$\boxed{(cos^2\alpha-sin^2\alpha) *1=cos2\alpha=LHS}$