Question

3-tg²10π/3*соs(4(x-7π/2))+8/cos²9π/4*sin(5π/2-2x)=0

Answer 1

$3-{\rm tg}\,^2\frac{\pi}{3}\cdot\cos(4(x-\frac{7\pi}{2}))+8\cos^2\frac{9\pi}{4}\cdot\sin(\frac{5\pi}{2}-2x)=0;\\ 3-3\cdot\cos(4x-14\pi)+8\cos^2\frac{\pi}{4}\cdot\sin(\frac{\pi}{2}-2x)=0;\\ 3+3\cdot\cos 4x+4\cdot\cos 2x=0;\\ 3+3\cdot(2\cos^2 2x-1)+4\cos 2x=0;\\ 6\cos^2 2x+4\cos 2x=0;\\ 2\cos 2x(3\cos 2x+2)=0;\\ \left[ {{2x=\frac{\pi}{2}+\pi n, n\in Z,} \atop {2x=\pm \arccos(-\frac{3}{2})+2\pi k, k\in Z}} \right.$
$\left[ {{x=\frac{\pi}{4}+\frac{\pi n}{2}, n\in Z,} \atop {x=\pm \frac{1}{2}\arccos(-\frac{3}{2})+\pi k, k\in Z}} \right.$