(sinx+cosx)^2=sin(5п/6)

Question

(sinx+cosx)^2=sin(5п/6)

Answer 1

Sin²x + 2SinxCos x + Cos²x = 1/2
1 + Sin2x = 1/2
Sin 2x = 1/2 -1
Sin 2x = -1/2
2x = (-1)^n arcSin(-1/2) + nπ, n∈Z
2x = (-1)^n·(-π/6) + nπ, n∈Z
2x = (-1)^(n+1) π/6 + nπ, n∈Z
x = (-1)^(n+1) π/12 + πn/2, n∈Z