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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.

\( \frac{\tan(\theta)}{\sin(\theta)} \) is equivalent to which of these?

If this equation is true...

\[ \sin^a(\theta) \cdot \csc^5(\theta) = \sin(\theta) \]

...then what is \(a\)?

Simplify:

\[ \sin^2(\theta) \csc^3(\theta) \cos^4(\theta) \sec^5(\theta) \tan^6(\theta) \cot^{7}(\theta) \]

\[ \frac{\sin^2(\theta) + 1}{\sin(\theta)} \]

Which expression is equivalent to the expression above?

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