Question

cos2x - sin^2(p/2-x) = -0.25
Решить уравнение.

Answer 1

2cos²x-1-cos²x=-0,25
cos²x-0,75=0
(cosx-√3/2)(cosx+√3/2)=0
cosx=√3/2⇒x=+ -π/6+2πn
cosx=-√3/2⇒x=+ -5π/6+2πn

Answer 2

cos2x - sin^2(p/2-x) = -1/4
cos2x   -   (1-cos(2(p/2-x)))/2 = -1/4
(2cos2x - 1  - cos2x) /2 = -1/4
(cos2x - 1)/2 = -1/4
cos2x=12
2x= ±π/3 + 2πn
x= ±π/6 + πn
n ∈ Z