16 sin^2 x = 16 − 8 cos x

Question

Find all solutions of the equation in the interval [0, 2π)

Answer 1

set
sin²(x) = 1-cos²(x)

16(1-cos²(x))=16-8cos(x)
and substitute c=cos(x)
16c²-8c=0
c(2c-1)=0
c=0 or c=1/2
Find all solutions for c=0 in [0,2π) and all solutions for c=1/2 in [0,2π).
Substitute back the solution and check that they are valid.