Question

sin²x/4-cos²x/4=1/2

Answer 1

Решение
sin²x/4-cos²x/4=1/2
- (cos²x/4 - sin²x/4) = 1/2
cos²x/4 - sin²x/4 = - 1/2
cos[2*(x/4)] = - 1/2
cosx/2 = - 1/2
x/2 = +-arccos(-1/2) + 2πk, k ∈ Z
x/2 = +- [π - arccos(1/2)] + 2πk, k ∈ Z
x/2 = +- [π - π/3)] + 2πk, k ∈ Z
x/2 = +- [2π/3)] + 2πk, k ∈ Z
x = +- [4π/3)] + 4πk, k ∈ Z