Geometry
# Proving Trigonometric Identities

Simplify

$\sin \theta \cos ^2 \theta - \sin \theta .$

Simplify

$\displaystyle \frac{1}{\sin^2 \theta}+\frac{1}{\cos^2 \theta}.$

Simplify

$\frac{ \tan ^2 \theta } { \tan ^2 \theta + 1 } .$

Which of the following is equal to the above expression?

Simplify

$\cos ^4 \theta + \sin^2 \theta \cos^2 \theta.$