Question

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

Answer 1

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