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Math Help - Simplifying math identity

  1. #1
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    Simplifying math identity

    this problem has been bugging me for a long time

    1/1-secx + 1/1+secx

    i keep ending up with 2/1-sec^2(x)

    but the answer is -2cot^2(x)

    can anybody help what am i doing wrong
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  2. #2
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    Quote Originally Posted by something3k View Post
    this problem has been bugging me for a long time

    1/1-secx + 1/1+secx

    i keep ending up with 2/1-sec^2(x)

    but the answer is -2cot^2(x)

    can anybody help what am i doing wrong
    Did you know:  1 + tan^2 x = sec^2 x ?

    If you don't want to use that identity I suggest you write the expression as  \frac{1}{1-\sec x} + \frac{1}{1+\sec x} = \frac{1}{\frac{\cos x -1}{\cos x}} + \frac{1}{\frac{\cos x +1}{\cos x}} = \frac{\cos x}{\cos x -1}+ \frac{\cos x}{\cos x +1} first.
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  3. #3
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by something3k View Post
    this problem has been bugging me for a long time

    1/1-secx + 1/1+secx

    i keep ending up with 2/1-sec^2(x)

    but the answer is -2cot^2(x)

    can anybody help what am i doing wrong
    so, you have \frac{2}{1-sec^{2}x}

    sex^2x-tan^2x=1

    so,

    tan^2x = sec^2x -1

    -tan^2x = -sec^2x+1 =1-sec^2x

    so your denominator is equivalent to -tan^2x, thus giving you

    \frac{2}{-tan^2x} = -2cot^2x [because  cotx = \frac{1}{tanx}]
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