Решите уравнение 5*(1/5)^соs2x=5^sin2x

Question

Решите уравнение 5*(1/5)^соs2x=5^sin2x

Answer 1

5·5^-Cos 2x = 5^Sin2x
5^(1-Cos 2x) = 5^Sin 2x
1 - Cos2x = Sin 2x
Sin 2x + Cos 2x = 1|²
Sin²2x + 2sin2x Cos 2x + Cos²2x = 1
1 + Sin 4x = 1
Sin 4x = 0
4x = π n, n∈Z
x = πn/4 , n∈Z