Question

sin2x+2cosx=sinx+1
cos2x+sinx=cos^2x помогите

Answer 1

$sin2x+2cos x=sin x+1\ 2sin xcos x+2cos x=sin x+1\ 2cos x(sin x+1)=sin x+1\ (sin x+1)(2cos x-1)=0\ left[begin{array}{ccc}sin x=-1\ cos x=0.5end{array}rightRightarrow~~~~ left[begin{array}{ccc}x_1=- frac{pi}{2}+2 pi k,k in mathbb{Z}\ x_2=pm frac{pi}{3}+2 pi n,n in mathbb{Z} end{array}right$

$cos 2x+sin x=cos^2x\ 1-2sin^2x+sin x=1-sin^2x\ sin^2x-sin x=0\ sin x(sin x-1)=0\ left[begin{array}{ccc}sin x=0\ sin x=1end{array}right~~Rightarrow~~~~~ left[begin{array}{ccc}x_1= pi k,k in mathbb{Z}\ x_2= frac{pi}{2}+2 pi k,k in mathbb{Z} end{array}right$