Question

РЕШЕНИЕ С ПОМОЩЬЮ СИСТЕМ 
$\sqrt{8-10cosx} =2sinx$

Answer 1

$\sqrt{8-10cosx}=2sinx\\ 8-10cosx=4sin^2x\\ 8-10cosx>0\\ cosx<\frac{4}{5}\\ 8-10cosx=4(1-cos^2x)\\\ 8-10cosx=4-4cos^2x\\ 4cos^2x-10cosx+4=0\\ D=100-4*4*4=6^2\\ x=\frac{10+6}{8}=2>1\\ x=\frac{10-6}{8}=\frac{1}{2}\\ x=\frac{\pi}{3}+2\pi*k$