Докажите тождество 1+2cosx+cos2x/1+cos2x-2cosx=-ctg^2 x/2

Question

Докажите тождество 1+2cosx+cos2x/1+cos2x-2cosx=-ctg^2 x/2

Answer 1

1+2cosx+cos2x/1+cos2-2cosx=2cos²+2cosx/2cos²x-2cosx=2cosx(cosx+1)/2cosx(cosx-1)= (cosx+1)/(cosx-1)=(2cos^2x/2)/(-2sin^2x/2)=-ctg^2x/2.