2 sin^2 theta = 3(cos theta +1)

Question

I am trying to solve this problem but i am having a hard time

Answer 1

2sin²θ=3(cosθ+1),

2(1-cos²θ)=3cosθ+3,

2-2cos²θ=3cosθ+3,

2cos²θ+3cosθ+1=0=(2cosθ+1)(cosθ+1).

So cosθ=-½ or -1. There are many solutions because of the cyclic nature of cosine.

If θ is between 0 and 360°, then θ=120° and 240°, and 180°.