Question

решить уравнение :cos^2x+6sinx-6=0

Answer 1

$cos^2x+6sin x-6=0\ 1-sin^2x+6sin x-6=0\ -sin^2x+6sin x-5=0|cdot(-1)\ sin^2 x-6sin x+5=0\ sin^2x-6sin x+9-4=0\ (sin x-3)^2=4\ left[begin{array}{ccc}sin x-3=2\ sin x-3=-2end{array}rightRightarrow left[begin{array}{ccc}sin x=5\ sin x=1end{array}rightRightarrow left[begin{array}{ccc}o\ x= frac{pi}{2}+2 pi k,k in mathbb{Z} end{array}right$