![image](https://tex.z-dn.net/?f=%5Csqrt%7B8-10cosx%7D%3D2sinx%5C%5C%0A8-10cosx%3D4sin%5E2x%5C%5C%0A8-10cosx%3E0%5C%5C%0Acosx%3C%5Cfrac%7B4%7D%7B5%7D%5C%5C%0A8-10cosx%3D4%281-cos%5E2x%29%5C%5C%5C%0A8-10cosx%3D4-4cos%5E2x%5C%5C%0A4cos%5E2x-10cosx%2B4%3D0%5C%5C%0AD%3D100-4%2A4%2A4%3D6%5E2%5C%5C%0Ax%3D%5Cfrac%7B10%2B6%7D%7B8%7D%3D2%3E1%5C%5C%0Ax%3D%5Cfrac%7B10-6%7D%7B8%7D%3D%5Cfrac%7B1%7D%7B2%7D%5C%5C%0Ax%3D%5Cfrac%7B%5Cpi%7D%7B3%7D%2B2%5Cpi%2Ak%5C%5C%0A)
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\\
" alt="\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\\
" align="absmiddle" class="latex-formula">