Question

решите уравнение
2-3 sin(3п/2+x)+cos^2 x/2=sin^2 x/2

Answer 1

$2-3 sin( \frac{3 \pi }{2} +x)+cos^2 \frac{x}{2} =sin^2 \frac{x}{2} \\ 2 + 3 cos x+cos^2 \frac{x}{2} = sin^2 \frac{x}{2} \\ 2 + 3 cos 2\frac{x}{2} +cos^2 \frac{x}{2} = sin^2 \frac{x}{2} \\ 2 + 3 (cos^2 \frac{x}{2} - sin^2 \frac{x}{2}) +cos^2 \frac{x}{2} = sin^2 \frac{x}{2} \\ 2 + 3 cos^2 \frac{x}{2} - 3sin^2 \frac{x}{2} +cos^2 \frac{x}{2} = sin^2 \frac{x}{2} \\ 2 + 4 cos^2 \frac{x}{2} - 4sin^2 \frac{x}{2} = 0 \\ 2 + 4 (cos^2 \frac{x}{2} - sin^2 \frac{x}{2} )= 0$
$2 + 4 cosx = 0 \\ 4 cosx = -2 \\ cosx = - \frac{1}{2} \\ x= +- \frac{2 \pi }{3} + 2 \pi k$