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[PreCalculus] Proving Identities

  1. Oct 16, 2009 #1
    1. The problem statement, all variables and given/known data
    Prove that this is an identity.

    1 + cos² x / sin² x = 2csc² - 1

    2. Relevant equations
    cos²x + sin²x = 1 (manipulative equation)
    tan²x = sec² - 1
    cot²x = csc²x - 1
    etc..

    3. The attempt at a solution
    I attempted this equation more than 10+ times. Each time, I find a way but I get half way there and it doesn't work out.
     
  2. jcsd
  3. Oct 16, 2009 #2

    rl.bhat

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    Homework Helper

    Hi Snowglober, welcome to PF
    The problem should be
    (1 + cos^2x)/sin^2x = 2csc^2x - 1
    Now LHS can be written as
    1/sin^2x + cos^2x/sin^2
    = csc^2x + cot^2x
    Now use the identities to get the result.
     
  4. Oct 18, 2009 #3
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