Find all the solutions of the function?

Question

2 sin^2 x = -1 + 3 sinx , find all solutions

Answer 1

Let y= sin(x).  Then this becomes

2y^2 = - 1 + 3y

2y^2 - 3y + 1 = 0

(2y - 1)(y - 1) = 0

So y = 1/2, 1

Ths means sin(x) = 1/2, 1

So x = pi/6, pi/2, etc.  I'll leave the general expression up to you.

Answer 2

let t=sin x.

==>

2t^2-3t+1=0

==>

t=1 or t=1/2.

sinx=1 ==>x=(2k+1/2)Pi

sinx=1/2

==>

x=(2k+1/6)Pi or (2k+5/6)Pi

Answer 3

sin(x) = 1/2, 1

So x = pi/6, pi/2, etc.