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Math Help - verify an identity

  1. #1
    Senior Member pacman's Avatar
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    verify an identity

    verify this identity: tan (45 + A) + tan (45 - A) = 2 sec (2A).
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  2. #2
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    Grandad's Avatar
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    Hello pacman
    Quote Originally Posted by pacman View Post
    verify this identity: tan (45 + A) + tan (45 - A) = 2 sec (2A).
    \tan(45+A)+\tan(45-A) = \frac{\tan45+\tan A}{1-\tan45\tan A}+\frac{\tan45-\tan A}{1+\tan45\tan A}

    =\frac{1+\tan A}{1-\tan A}+\frac{1-\tan A}{1+\tan A}

    =\frac{(1+\tan A)^2 +(1-\tan A)^2}{(1+\tan A)(1-\tan A)}

    = \frac{2+2\tan^2A}{1-\tan^2A}

    = \frac{2\cos^2A+2\sin^2A}{\cos^2A - \sin^2A}

    =\frac{2}{\cos2A}

    =2\sec2A

    Grandad
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  3. #3
    Senior Member pacman's Avatar
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    That's a clean sweep Grandad, Thanks!
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