ShmoopTube

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For a good time, solve this shmoopy question.

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Simplify. sin4⍺ - cos4⍺ << sine to the fourth alpha minus cosine to the fourth alpha>>

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And here are our answer choices...

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Okay, the trick lies in recognizing the fact that 2 squared equals 4.

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It means we can express sine to the fourth alpha minus cosine to

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the fourth alpha as sine squared alpha squared

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minus cosine squared alpha squared... because they're the same thing.

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Now we need to call on our good friend - the

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difference of two squares formula: x squared minus y squared equals x minus y times x plus y.

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If we pretend that sin squared alpha is x

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and cos squared alpha is y, we can simplify it to:

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sin squared alpha minus cosine squared alpha times sin squared alpha PLUS cosine squared

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alpha. We also know that (sin2⍺

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+ cos2⍺) = 1 from the fundamental trig identities.

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Now all we're left with is (sin2⍺ -- cos2⍺)...

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...which happens to be answer D.

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