5+sin x= 5 cis 2x Уравнение

[latex]5+sinx=5cos2x \\ 5+sinx=5cos^{2}x-5sin^{2}x \\ 5+sinx=5(1-sin^{2}x)-5sin^{2}x \\ 5+sinx=5-10sin^{2}x \\ 5+sinx-5+10sin^{2}x=0 \\ 10sin^{2}x+sinx=0 \\ sinx(10sinx+1)=0 \\ \\ 1)sinx=0 \\ x=\pi n,n\in Z; \\ \\ 10sinx+1=0 \\ 10sinx=-1 \\ sinx=- \frac{1}{10} \\ x=(-1)^{n+1}arcsin \frac{1}{10}+2\pi n,n\in Z. [/latex]