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Math Help - Prove the following

  1. #1
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    Prove the following

    Please view attachment!!!
    Attached Thumbnails Attached Thumbnails Prove the following-image0350.jpg  
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  2. #2
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    Re: Prove the following

    Hey anil86.

    I'd suggest you take a look at the sum-to-product and product-to-sum identities (and keeping in mind the relation cos(ix) and cosh(x) and so on).

    List of trigonometric identities - Wikipedia, the free encyclopedia
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  3. #3
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    Re: Prove the following

    Restating the problem:Given
    \sin (\theta +i \varphi )=\tan  \alpha  + i \sec  \alpha
    or
    \sin  \theta  \cosh  \varphi  = \tan  \alpha
    \cos  \theta  \sinh  \varphi  = \sec  \alpha
    Show
    \cos  2\theta  \cosh  2\varphi  = 3

    Let
    a=\cos ^2\theta \text{  } and b=\sin ^2\theta

    c=\cosh ^2\varphi and d=\sinh ^2\varphi

    so that

    a+b=1

    c-d=1

    a d - b c = 1

    a-b=\cos  2\theta

    c+d= \cosh  2\varphi

    Now use the identity

    (a-b)(c+d)=2(a d-b c)+(a+b)(c-d)
    Last edited by Idea; November 24th 2013 at 02:50 AM.
    Thanks from anil86
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