Proving Trigonometric Identities

Proving Trigonometric Identities Warmup


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

If this equation is true...

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

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


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

How many ways are there to fill the blanks so the equation is true, choosing from the six basic trigonometric functions (sin, cos, tan, csc, sec, cot)?

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

Which expression is equivalent to the expression above?


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