1.Simplify the expression: cos^2 theta- cos^4 theta/ tan theta

2 answers

assuming you meant:
(cos^2 θ- cos^4 θ)/ tan θ
= cos^2 θ(1 - cos^2 θ)/tan θ
= cos^2 θ sin^2 θ / (sinθ/cosθ)
= cos^2 θ sin^2 θ cosθ/sinθ
= cos^2 θ sinθ
or
= (1 - sin^2 θ) sinθ
= sinθ - sin^2 θ
Hmmm.
= cos^2 θ sin^2 θ cosθ/sinθ
= cos^3 θ sinθ
or
cos^2θ sinθ cosθ
(1+cos2θ)/2 * 1/2 sin2θ
= (1 + cos2θ)sin2θ/4
or
sin2θ/4 + sin4θ/8