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# Proving Trigonometric Identities

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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