Question

cos^2 x -0,5sin 2x =1

Answer 1

$\cos^2x-0.5\sin 2x=1 \\ \cos^2x-0.5\cdot 2\sin x\cos x=\cos^2x+\sin^2x \\ -\sin x\cos x-\sin^2x=0 \\ -\sin x(\cos x+\sin x)=0 \\ \left[\begin{array}{ccc}\sin x=0\\ tg x=-1\end{array}\right\to \left[\begin{array}{ccc}x_1= \pi k,k \in Z\\ x_2=- \frac{\pi}{4} + \pi n,n \in Z\end{array}\right$