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Math Help - Prove that

  1. #1
    Newbie Sanjana Das's Avatar
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    Question Prove that


    [1+cosA+sinA] = 1+sinA
    [1+cosA-sinA] ... cosA

    plzzzzz help meeee .......with this question....
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  2. #2
    Super Member malaygoel's Avatar
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    Quote Originally Posted by Sanjana Das View Post
    [1+cosA+sinA] = 1+sinA
    [1+cosA-sinA] ... cosA

    plzzzzz help meeee .......with this question....

    \frac{1+cosA+sinA}{1+cosA-sinA}

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

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

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

    = \frac{1+sinA}{cosA}
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  3. #3
    Super Member malaygoel's Avatar
    Joined
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    India
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    Quote Originally Posted by Sanjana Das View Post
    [1+cosA+sinA] = 1+sinA
    [1+cosA-sinA] ... cosA

    plzzzzz help meeee .......with this question....
    \frac{1+cosA+sinA}{1+cosA-sinA}.\frac{cosA-sinA-1}{cosA-sinA-1}

    = \frac{cos^2A-sin^2A-2sinA-1}{-2sinAcosA}

    = \frac{1+sinA}{cosA}
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