Question

Докажите тождество
cos(2π-x)cos^2(0,5π+x)/tg(x-π)sin(0,5π+x)=0,5sin2x

Answer 1

$\frac{\cos (2\pi -x)\cos^2(0.5\pi +x)}{tg(x-\pi )\sin (0.5\pi +x)} = \frac{\cos x\sin ^2x}{tg x\cos x} = \frac{\sin^2x\cos x}{\sin x} =\sin x\cos x=0.5\sin 2x$