Question

решить уравнение
-cos2x - 1=3 cos (7пи/2-x)

Answer 1

cos(7П/2-x)=cos(3П/2-x)=-sinx
-cos2x-1=-3sinx
cos2x+1=3sinx
1-2sin^2x+1=3sinx
2sin^2x+3sinx-2=0
sinx=t
-1<=t<=1
2t^2+3t-2=0
t=-3+-√(9+16)/4=(-3+-5)/4
t=1/2
sinx=1/2
x=(-1)^kП/6+Пk