-2sin(x-7П/2)*sin x = корень из 3*cos x

Question

-2sin(x-7П/2)*sin x = корень из 3*cos x

Answer 1

-2*sin(x - 7π/2)*sinx = √3*cosx
-2*sin(x - (4π - π/2))*sinx = √3*cosx
-2*sin(x - 4π + π/2)*sinx = √3*cosx
-2*sin(x + π/2)*sinx = √3*cosx
-2*cosx*sinx - √3*cosx = 0
cosx*(2sinx + √3) = 0
1) cosx = 0
x = π/2 + πk
2) 2sinx + √3 = 0
sinx = -√3/2
x = -π/3 + 2πk
x = -2π/3 + 2πk