Question

Solve the equation on the interval [0,2pi)

2cos² θ/2 -3cosθ=0

Answer 1

to solve this problem, you first have to know the half angle identify of cosine.
cos(θ/2)=+/-√(1+cosθ)/2, so cos² (θ/2)=(1+cosθ)/2, and 2cos² (θ/2)=1+cosθ

2cos² (θ/2) -3cosθ=0
1+cosθ-3cosθ=0
2cosθ=1
cosθ=1/2
θ=π/3, or (5/3)π