Solve the equation 2cos2x + 4sinx = 3.

We have to solve 2*cos 2x + 4*sin x =
3.

We use the relation: cos 2x = 1 – 2* (sin
x)^2

2*cos 2x + 4*sin x =
3

=> 2* (1 – 2* (sin x)^2) + 4*sin x =
3

=> 2 – 4*(sin x)^2 + 4* sin x =
3

let y = sin x

=> 4y^2
– 4y + 1 = 0

=> (2y – 1)^2 =
0

=> 2y = 1

=> y
= 1/2

As y = sin x , sin x = 1/2 or x = arc sin (1/2) =
pi/6 + 2*n*pi and x = 5*pi/6 + 2*n*pi

We get
x = pi/6 + 2*n*pi and x = 5*pi/6 + 2*n*pi.