So, you've memorized your fundamental identities, but how can you prove the more obscure ones? See how to apply the basic building blocks of trig to understand deeper relationships.

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

\[ \cos ^4 \theta + \sin^2 \theta \cos^2 \theta. \]

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