Question

Решите уравнение $cos^{2} frac{x}{3} + sin ^{4} frac{x}{3} = 1$

Answer 1

(1+cos(2x/3))/2+(1-cos(2x/3))²/4=1
2+2cos(2x/3)+1-2cos(2x/3)+cos²(2x/3)=4
cos²(2x/3)=1
(1+cos(4x/3))/2=1
1+cos(4x/3)=2
cos(4x/3)=1
4x/3=2πn
x=3πn/2,n∈z