Question

Упростите выражение cos^2/tg(x/2)-ctg(x/2)......

Answer 1

$\frac{cos^2x}{tg \frac{x}{2}-ctg \frac{x}{2} }= \frac{cos^2x}{ \frac{sin \frac{x}{2} }{cos \frac{x}{2} } - \frac{cos \frac{x}{w} }{sin \frac{x}{2} } }= \frac{cos^2x}{ \frac{sin^2 \frac{x}{2}-cos^2 \frac{x}{2} }{sin \frac{x}{2}*cos \frac{x}{2} } }= \frac{cos^2x*2sin \frac{x}{2}*cos \frac{x}{2} }{-2(cos^2 \frac{x}{2}-sin^2 \frac{x}{2}) }= \\\\= \frac{cos^2x*sin(2* \frac{x}{2}) }{-2cos(2* \frac{x}{2}) } = \frac{cos^2x*sinx}{-2cosx}=- \frac{1}{2}sinx*cosx=\\\\=- \frac{1}{4}*(2sinx*cosx)=-0,5sin2x$