Question

Решите уравнения: Cos 2x + 3sin x = 1

Answer 1

$cos2x+3sinx=1 \\ cos2x=1-2sin^2x \\ 1-2sin^2x+3sinx=1 \\ 2sin^2x-3sinx=0 \\ sinx=t \\ 2t^2-3t=0 \\ \left \{ {{t_1=0} \atop {t_2=\frac{3}{2}}} \right. \left \{ {{sinx=0} \atop {sinx=\frac{3}{2}}} \right. \left \{ {{x_1=\pi n} \atop {x_2=\pi+2\pi n}} \right.$

,n∈Z.