ShmoopTube

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And here is your shmoop de jour.

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Simplified tangents squared alpha over sine squared alpha minus 1

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And here are the potential answers...

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Okay well whenever we see a tangent we can change

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to sine over cosine. Now we have a triple layer fraction cake.

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To get rid of it, we multiply by one over sin squared alpha

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The sines squared alpha cancels out on the top and bottom like this

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which leaves us with one over cosine squared alpha -1

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cosine and secant are inverse functions

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so 1 over cosine squared alpha is the same thing

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as secant squared alpha and the handy dandy trig identity

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1 plus tangent squared alpha equals secant squared alpha

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can be rearranged to become secant squared alpha -1

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equals tangent squared alpha. What do you know? We're left with secant squared alpha

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-1 in our expression

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and we just figured out secant squared alpha -1 equals tangent squared alpha.

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Which is option E.

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