Question

2cos^2 (3x) + sin5x = 1

Answer 1

Sin 5x = 1 - 2Cos² 3x
Sin 5x = - Cos 6x
Sin 5x + Cos 6x = 0
Sin 5x + Sin(π/2 - 6x) = 0
2Sin(π/4 - х/2)Сos( 11x/2 - π/4) = 0
а) Sin (π/4 - х/2) = 0        или         б) Cos(11x/2 - π/4) = 0
 π/4 - х/2 = πn, n∈Z                           11x/2 - π/4 = π/2 + πк, к ∈Z
-x/2 = πn + π/4, n ∈Z                         11x/2 = π/2 + π/4 + πк, к∈Z
x = -2πn - π/2, n ∈Z                            x = 3π/22 + 2πк/11, к ∈Z