Square both sides:
4cos2x = sin2x + 2sinx + 1
Replace cos2 by 1 - sin2
4(1 - sin2x) = sin2x + 2sinx + 1
Collect terms
5sin2x + 2sinx - 3 = 0
This can be written as
(sinx + 5/5)(sinx - 3/5) = 0 or (sinx + 1)(sinx - 3/5) = 0
So sinx = -1 and sinx = 3/5
This means x = asin(-1) = 3pi/2 (=270°)
and x = asin(3/5) ≈ 36.87°
Adding and subtracting multiples of 2pi (360°) to these also satisfies the original equation.
.
Square both sides:
4cos2x = sin2x + 2sinx + 1
Replace cos2 by 1 - sin2
4(1 - sin2x) = sin2x + 2sinx + 1
Collect terms
5sin2x + 2sinx - 3 = 0
This can be written as
(sinx + 5/5)(sinx - 3/5) = 0 or (sinx + 1)(sinx - 3/5) = 0
So sinx = -1 and sinx = 3/5
This means x = asin(-1) = 3pi/2 (=270°)
and x = asin(3/5) ≈ 36.87°
Adding and subtracting multiples of 2pi (360°) to these also satisfies the original equation.
.