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Math Help - trig identities help needed

  1. #1
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    trig identities help needed

    so i have my end of prelims coming up and doing a revision test. this question came up

     prove (sec^2x - 1)cos^2x = sin^2x
    Now i thought that you would do the question like this:

    LHS = (sec^2x-1)cos^2x = (Tan^2x)cos^2x<br />
                                         = \frac{\sin^2x}{cos^2x} cos^2x<br />
                                         =sin^2x<br />

    but it gave a different soln. am i wrong?
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  2. #2
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    Quote Originally Posted by link0099 View Post
    so i have my end of prelims coming up and doing a revision test. this question came up

     prove (sec^2x - 1)cos^2x = sin^2x
    Now i thought that you would do the question like this:

    LHS = (sec^2x-1)cos^2x = (Tan^2x)cos^2x<br />
                                         = \frac{\sin^2x}{cos^2x} cos^2x<br />
                                         =sin^2x<br />

    but it gave a different soln. am i wrong?
    Your proof is valid. The book most likely uses \sin^2x+\cos^2x=1 which of course if you divide through by \cos^2x gives the identity you used.
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  3. #3
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    oh good, thanks a lot
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