Question

2 cos x + sin 2x = 0

Answer 1

Find all solutions to the equation in the interval [0, 2π)

Answer 2

sin2x = 2sinx cosx

2cosx + 2sinx cosx = 0
2cosx (1 + sinx) = 0
1 + sinx = 0 OR 2cosx = 0-> cosx=0
sinx = -1 x= 90, 270 = π/2 , 3π/2
x = 270 = 3π/2

so the solutions -> x = π/2 , 3π/2