ShmoopTube

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Here's your shmoop du jour, brought to you by Alpha. Please don't tell it that it looks

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like a "cute little fishie." It hates that.

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Simplify: 2sin alpha over cos alpha times the quantity 1 minus tan squared alpha.

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And here are your potential answers...

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Alright, we're going to have to work with

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a lot of trig here to simplify this... if you aren't too great with your trig formulas

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and identities, we'd recommend you hit pause and review them before you tackle this problem.

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formula is just too messy...

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formula is just too messy...

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So… let's start simplifying it first.

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Ok, here goes. First we can separate this nasty thing into two fractions multiplied

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by each other

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This gives us 2 times sine alpha over cosine alpha times 1 over the quantity 1 minus tangent

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squared alpha. Because we know our identities backward and

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forward, we know that tangent alpha equals sin alpha over cosine alpha...

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...leaving us with 2 times tangent alpha over the quantity 1 minus tangent squared alpha.

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But wait - doesn't that look like our formula for tangent 2 alpha?

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Why yes, it does. Tangent 2 alpha is our answer. Answer E.

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