solve equation 22 sin theta 4 cos2 theta Solve the equation

Solve the equation 2-2 sin theta = 4 cos2 theta What is the solution in the interval 0

Solution

2-2sin = 4cos²

cos²+sin²=1 is identity =>cos²=1-sin²

2-2sin = 4(1-sin²)

1-sin = 2(1-sin²)

1-sin = 2-2sin²

2sin²-sin-1 = 0

2sin²-2sin+sin-1 = 0

2sin(sin-1) +1(sin-1)=0

(sin-1)(2sin+1)=0

sin=1,sin=-1/2

sin=1=>=/2

sin=-1/2=>=7/6 ,11/6

solution is =/2,7/6 ,11/6