Proving Trigonometric Identities

Proving Trigonometric Identities Warmup


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

If this equation is true...

sina(θ)csc5(θ)=sin(θ) \sin^a(\theta) \cdot \csc^5(\theta) = \sin(\theta)

...then what is aa?


sin2(θ)csc3(θ)cos4(θ)sec5(θ)tan6(θ)cot7(θ) \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)?

sin2(θ)+1sin(θ) \frac{\sin^2(\theta) + 1}{\sin(\theta)}

Which expression is equivalent to the expression above?


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