Question

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

Answer 1

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