Question

sin^2(п/2-x)+cos x =0

Answer 1

$\sin {}^{2} ( \frac{\pi}{2} - x ) + \cos(x) = 0$

$\sin( \frac{\pi}{2} - x ) = \sin( \frac{\pi}{2} ) \cos(x) - \cos( \frac{\pi}{2} ) \sin(x) = \cos(x)$

$\cos {}^{2} (x) + \cos(x) = 0 \\ \cos(x) ( \cos(x) + 1) = 0 \\ \cos(x) = 0 \\ \cos(x) = - 1 \\ x = \frac{\pi}{2} + \pi n \\ x = \pi + 2\pi n$