Question

Please help! Verify the identity: 1-cos2x=tanx sin2x

Answer 1

\[(1-\cos 2x) \cdot \frac{ (1+\cos 2x }{ 1 + \cos 2x }=\frac{ 1-\cos^2 2x }{ 1+\cos 2x }=\frac{ \sin^2 2x }{ 1+\cos 2x }=\frac{ \sin 2x }{ 1+\cos 2x }\cdot \sin 2x\]\[=\frac{ 2\sin x \cos x }{ 1+(2\cos^2 x-1) }\cdot \sin 2x=\frac{ 2\sin x \cos x }{ 2\cos^2 x }\cdot \sin 2x\]

you should be able to finish it from here...