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Math Help - Trigonometry Identity

  1. #1
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    Trigonometry Identity

    tan2\theta- sin2\theta = x and tan2\theta + sin2\theta = y prove that (x^2 -y^2)^2 = 16xy
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  2. #2
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    I revise

    I revise : tan2\theta- sin2\theta = x and tan2\theta + sin2\theta = y prove that (x^2 -y^2)^2 = 16xy
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  3. #3
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    Hello wizard654zzz
    Quote Originally Posted by wizard654zzz View Post
    I revise : tan2\theta- sin2\theta = x and tan2\theta + sin2\theta = y prove that (x^2 -y^2)^2 = 16xy
    Factorise the LHS using difference of two squares:
    (x^2-y^2)^2
    =\Big((x+y)(x-y)\Big)^2

    =\Big(2\tan2\theta(-2\sin2\theta)\Big)^2

    = 16\tan^22\theta\sin^22\theta

    =16\tan^22\theta(1-\cos^22\theta)

    =16(\tan^22\theta-\tan^22\theta\cos^22\theta)

    =16(\tan^22\theta-\sin^22\theta)

    =16(\tan2\theta - \sin2\theta)(\tan2\theta +\sin2\theta)

    =16xy
    Grandad
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  4. #4
    Junior Member mrmohamed's Avatar
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    Quote Originally Posted by wizard654zzz View Post
    I revise : tan2\theta- sin2\theta = x and tan2\theta + sin2\theta = y prove that (x^2 -y^2)^2 = 16xy
    hi all

    another methode
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