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vittoria

  • 3 years ago

cot x sec^4x = cot x + 2 tan x + tan^3x this is the problem I need to simplify. I'm not certain whether I can think of something like 2 tan as tan^2. I'm also having problems finding identities that will help me. Thank you so much!

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  1. wio
    • 3 years ago
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    What happens when you sub \(\sec^2(x) = \tan^2(x)+1\)?

  2. wio
    • 3 years ago
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    Since \(\sec^4(x) = [\sec^2(x)]^2\)

  3. vittoria
    • 3 years ago
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    So i can use that formula, but instead of tan^2(x) + 1. I do [tan^2(x) + 1]^2?

  4. wio
    • 3 years ago
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    Exactly

  5. wio
    • 3 years ago
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    Then foil it out and see if you've gotten closer.

  6. vittoria
    • 3 years ago
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    cot x [tan^2(x) + 1]^2 = cot x + 2 tan x + tan^3x which turns into : cot x tan^4(x^2) + 1 = cot x + 2 tan x + tan^3x correct?

  7. wio
    • 3 years ago
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    Not quite... \[ [\tan^2(x)+1]^2 = [\tan^4(x) + 2\tan^2(x) + 1] \]

  8. wio
    • 3 years ago
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    Since \(\cot(x) = 1/\tan(x)\) it will basically lower the power of the \(\tan(x)\) terms.

  9. vittoria
    • 3 years ago
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    Sorry, I'm not sure where you got the 2 tan ^2 from

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