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Math Help - Need help in solving trigo an

  1. #1
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    [Solved] Need help in solving trigo an

    Given that tan(2A) = (2tanA)/(1-tan^2 A)

    show that tan(22.5) = sqrt(2) - 1
    Last edited by ZGOON; September 23rd 2012 at 01:40 AM.
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Need help in solving trigo an

    Define A\equiv22.5^{\circ} and write the given double angle identity for tangent as:

    \tan(2(22.5^{\circ}))=\frac{2\tan(22.5^{\circ})}{1-\tan^2(22.5^{\circ})}

    \tan(45^{\circ})=\frac{2\tan(22.5^{\circ})}{1-\tan^2(22.5^{\circ})}

    1=\frac{2\tan(22.5^{\circ})}{1-\tan^2(22.5^{\circ})}

    Can you finish?
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  3. #3
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    Re: Need help in solving trigo an

    Quote Originally Posted by MarkFL2 View Post
    Define A\equiv22.5^{\circ} and write the given double angle identity for tangent as:

    \tan(2(22.5^{\circ}))=\frac{2\tan(22.5^{\circ})}{1-\tan^2(22.5^{\circ})}

    \tan(45^{\circ})=\frac{2\tan(22.5^{\circ})}{1-\tan^2(22.5^{\circ})}

    1=\frac{2\tan(22.5^{\circ})}{1-\tan^2(22.5^{\circ})}

    Can you finish?
    I managed to get that part...
    and i let tan(22.5) be Y
    it becomes eqn [y^2 + 2y - 1 = 0]
    but somehow i cant get the sqrt(2)

    *im using the cross multiply method to solve the eqn
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: Need help in solving trigo an

    You have the correct quadratic...now either complete the square or use the quadratic formula.

    You will get 2 roots. You will need to decide which is extraneous, either by substituting the roots into the original equation, or some knowledge of which quadrant the angle is in and what sign tangent has there...
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  5. #5
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    Re: Need help in solving trigo an

    Ohhhh! I'm im able to solve it now!!! THANKS THANKS THANKS!!!
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