[tex]\\2\cos^{2}x+7\sin x- 5 =0\\ -2\sin^2 x+2+7\sin x-5=0\\ -2\sin^2x+7\sin x-3=0\\ -2\sin^2 x+\sin x+6\sin x-3=0\\ -\sin x(2\sin x-1)+3(2\sin x-1)=0\\ -(\sin x-3)(2\sin x-1)=0\\ [/tex]
[tex]\\\sin x-3=0\\ \sin x=3\\ [/tex] ⇐ нет решения
[tex]\\2\sin x-1=0\\ 2\sin x=1\\ \sin x=\frac{1}{2}\\ x=\frac{\pi}{6}+2k\pi \vee x=\frac{5\pi}{6}+2k\pi\\ k\in \mathbb{Z}[/tex]
