Question

Помогите решить ............................

Answer 1

$1)f(x)=Cos^{2}\frac{x}{2}-Sin^{2}\frac{x}{2}=Cosx\\\\f'(x)=(Cosx)'=-Sinx\\\\f'(x)>0\\\\-Sinx>0\\\\Sinx<0\\\\\boxed{x\in(\pi+2\pi n ;2\pi+2\pi n),n\in Z}$

$2)f(x)=2Sin^{2}\frac{x}{2}- 2Cos^{2}\frac{x}{2} =-2(Cos^{2}\frac{x}{2}-Sin^{2}\frac{x}{2})=-2Cosx\\\\f'(x)=-2(Cosx)'=-2*(-Sinx)=2Sinx\\f'(x)>0\\\\2Sinx>0\\\\Sinx>0\\\\\boxed{x\in(2\pi n;\pi+2\pi n),n\in Z }$

$3)f(x)=x-Cosx\\\\f'(x)=x'-(Cosx)'=1-(-Sinx)=1+Sinx\\\\f'(x)>0\\\\1+Sinx>0\\\\Sinx>-1\\\boxed{x\in(-\frac{\pi }{2}+2\pi n;\frac{3\pi }{2}+2\pi n),n\in Z}$