Question

Prove a seguinte identidade:


$\frac{(senx + cosx)^{2} - (senx - cosx)^{2} }{4 . cosx} = sen x$

Answer 1

$\dfrac{(\sin x+\cos x)^2-(\sin x-\cos x)^2}{4\cos x}=\sin x\\\\ \dfrac{(\sin x+\cos x+\sin x-\cos x)[\sin x+\cos x-(\sin x-\cos x)]}{4\cos x}=\sin x\\\\ \dfrac{2\sin x\cdot2\cos x}{4\cos x}=\sin x\\\\ \dfrac{4\sin x\cos x}{4\cos x}=\sin x\\\\ \sin x=\sin x\Longrightarrow OK!$