Find all solutions of the equation 2sin2x 3 sin x 2 0 in

Find all solutions of the equation 2sin^2x + 3 sin x - 2 = 0 in [0,2pi]. Write your answer in radians in terms of pi.

Solution

Solution :

The equation may be written as:

2sin^2 x+ 4sin x -sin x -2=0

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

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

When 2sin-1=0, then sin x=1/2

Or. x = /6, 5/6. Ans.