Question

Find all the solutions of the equation in the interval 0 2pi) 2sin2x=2+cosx

Answer 1

Assuming you mean sin(x)^2 and not sin(2x),

2sin(x)^2 = 2 - 2cos(x)^2

2cos(x)^2 + cos(x) = 0

cos(x)(2cos(x) + 1) = 0

cos(x) = 0 or cos(x) = -1/2

x = π/2, 3π/2, 2π/3, 4π/3