Question

cosx=(cos(x/2)-sin(x/2))^2-1

Answer 1

$cos(x) = (cos(\frac{x}{2}) - sin(\frac{x}{2}))^{2} - 1\\ cos(x) = cos^{2}(\frac{x}{2}) - 2sin(\frac{x}{2})cos(\frac{x}{2}) + sin^{2}(\frac{x}{2}) - 1\\ cos(x) = -sin(x)\ |:sin(x)\\ ctg(x) = -1\\ => x = \frac{3\pi}{4} + \pi\cdot n$