if 0 smaller and equal θ smaller and equal 2 pi, solve: -2cos^2+2sin^2θ =2cos x

Question

if 0 smaller and equal θ smaller and equal 2 pi, solve: -2cos^2+2sin^2θ =2cos x

show works please

Answer 1

adds 4 cos^2 to both sides

2 cos^2 + 2sin^2 = 4 cos^2 + 2cos

2(cos^2+sin^2) = 4 cos^2 + 2 cos

2 = 4 cos^2 + 2 cos

1 = 2 cos^2 + cos

0 = cos^2 + cos - 1

0 = M^2 + M - 1

M = (-1 +or- sqrt( 1+4))/2

= (-1 +or- sqrt(5))/2

inverse cosines, the angle is close to 1