2*cos2x=sin(3*pi/2-x)-2. Created by ElviraS97. algebra-ru

2-x)-2...

Nyrsan По формуле приведения sin(3pi/2-x)=-cosx
2cosx=-cosx-2
3cosx=-2
cosx=-2/3
x=+-arcos(-2/3)

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мохинсан $2\cos2x=\sin(\frac{3\pi}{2}-x)-2;\\
4\cos^2x-2=\sin\frac{3\pi}{2}\cos x-\cos\frac{3\pi}{2}\sin x-2;\\
4\cos^2x-2=-\cos x-2;\\
4\cos^2x+\cos x=0;\\
t=\cos x;\ \ -1\leq t \leq1;\\
4t^2+t=0;\\
t(4t+1)=0;\\
t_1=0;\\
t_2=-\frac{1}{4};\\
\cos x =0;\ \ \ x_1=\frac{\pi}{2}+\pi n n\in Z;\\
\cos x=-\frac{1}{4};\ \ \ \ x=\pm\arccos(-\frac{1}{4})+2 \pi k, k\in Z$

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