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Homework Help: Proving trig identities!

  1. Jan 21, 2010 #1
    Can someone please help me with these two questions.

    Th first one is prove:

    1-tan^2x
    ________ = cos2x
    1+tan^2x

    & the second one is

    prove:

    sinx+ sinxcot^2 = secx
     
  2. jcsd
  3. Jan 22, 2010 #2

    1)

    1-tan^2x
    ________ = cos2x
    1+tan^2x


    LHS : [1 - (sin^2x/ cos^2x) ] / [ 1 + (sin^2x/cos^2x)]

    = [(cos^2x -sin^2x)/cos^2x] X [cos^2x/(cos^2x + sin^2x)]

    = (cos^2x - sin^2x) / (cos^2x +sin^2x ) (Rmb cos^2x + sin^2x =1 )

    = cos^2x -sin^2x

    = cos^2x - (1 - cos^2x)
    = 2cos^2x -1 (double angle formula)
    = cos2x = RHS



    for question 2, did you miss out an x beside cot^ ?
     
    Last edited: Jan 22, 2010
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