Question

Помогите, пожалуйста!

Answer 1

$cos(x+50)+sin(x+40)=1+2cosxsin40+cos90\\\\cosxcos50-sinxsin50+sinxcos40+cosxsin40=1+2cosxsin40+\\+cos90\\\\cosxcos(90-40)-sinxsin(90-40)+sinxcos40+cosxsin40=\\=1+2cosxsin40+cos90\\\\cosxsin40-sinxcos40+sinxcos40+cosxsin40=1+2cosxsin40+0\\\\2cosxsin40=1+2cosxsin40\\0=1$
Решений нет.

$cos\frac{x}{8}sin^3\frac{x}{8}-cos^3\frac{x}{8}sin\frac{x}{8}=\frac{\sqrt3}{8}\\sin\frac{x}{8}cos\frac{x}{8}(sin^2\frac{x}{8}-cos^2\frac{x}{8})=\frac{\sqrt3}{8}\\-\frac{1}{2}sin\frac{x}{4}cos\frac{x}{4}=\frac{\sqrt3}{8}\\-\frac{1}{4}sin\frac{x}{2}=\frac{\sqrt3}{8}\\sin\frac{x}{2}=-\frac{\sqrt3}{2}\\\frac{x}{2}=\frac{4\pi}{3}+2\pi n;n\in Z\ \ \ \ \ \ \ \ \ \ \ \ \ \frac{x}{2}=\frac{5\pi}{3}+2\pi n;n\in Z\\x=\frac{8\pi}{3}+4\pi n;n\in Z\ \ \ \ \ \ \ \ \ \ \ \ \ x=\frac{10\pi}{3}+4\pi n;n\in Z$