Решите, пожалуйста:
Cos x + sin x + sin2x + 1 = 0

$cos x+sin x+sin 2x+1=0 cos x+sin x+2sin xcos x+cos^2x+sin^2x=0 (cos x+ sin x)+(cos x +sin x)^2=0 (cos x+sin x)(1+cos x+sin x)=0$

$cos x+sin x=0|: cos x tg x=-1 x=- frac{pi}{4}+pi n,n in Z$

$cos x+sin x=-1$

Формула: $a sin xpm bcos x= sqrt{a^2+b^2} sin(xpm arcsin frac{1}{sqrt{a^2+b^2}} )$

$sqrt{a^2+b^2}= sqrt{2}$

$sqrt{2}sin (x+ frac{pi}{4} )=-1 sin(x+ frac{pi}{4} )=- frac{1}{sqrt{2}} x+frac{pi}{4}=(-1)^{k+1}cdot frac{pi}{4}+ pi k,k in Z x=(-1)^{k+1}cdot frac{pi}{4}-frac{pi}{4}+ pi k,k in Z$