Sin2x = 1 + √2cosx + cos2x
2sinxcosx = 1 + √2cosx + 2cos^2x - 1
2sinxcosx = √2cosx + 2cos^2x
2sinxcosx - √2cosx - 2cos^2x = 0
2cosx (sinx - √2/2 - cosx) = 0
1) 2cosx = 0
cosx = 0
x = pi/2+ pik, k ∈Z
2) sinx - √2/2 - cosx = 0
sinx - cosx = √2/2
(sinx - cosx)^2 = (√2/2)^2
sin^2x - 2cosxsinx + cos^2x = 2/4
1 - 2cosxsinx = 1/2
- 2cosxsinx = - 1/2
2cosxsinx = 1/2
sin2x = 1/2
2x = (-1)^n arcsin(1/2) + pik
x = (-1)^n * pi/12 + (pik)/2, k ∈ Z