Question

sin4x+cos4x=1 помогите пожалуйста!)

Answer 1

sin4x + cos4x = 1
2*sin(2x)cos(2x) + 1 - 2*(sin^2)(2x) = 1
2sin2x(cos2x - sin2x) = 0
1)  sin2x = 0
2x = πn, n∈Z
x1 = (πn)/2, n∈Z
2)  cos2x - sin2x = 0    /cos2x ≠ 0
1 - tg(2x) = 0
tg(2x) = 1
2x = π/4 + πk, k∈Z
x2 = π/8 + (πk)/2, k