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Math Help - trignometric identities

  1. #1
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    trignometric identities

    prove that:
    1. \frac{\sin A + \sin 2A}{\cos A - \cos 2A} =\cot (A/2)
    2. \frac{1+\cos A}{\sin A} = \cot (A/2)

    please help...
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  2. #2
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    Re: trignometric identities

    What have you tried to this point?

    I suggest thinking about some double angle formulas for the first question.
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    Re: trignometric identities

    i tried using the double angle formulas but dont know how to bring about the cot(A/2) for the first one .
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    Re: trignometric identities

    For the first one I think it can be useful to work with the identities:
    \sin(x)+\sin(y)=2\sin\left(\frac{x+y}{2}\right) \cos\left(\frac{x-y}{2}\right)
    \cos(x)-\cos(y)=-2\sin\left(\frac{x+y}{2}\right)\sin\left(\frac{x-y}{2}\right)
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  5. #5
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    Re: trignometric identities

    i did the fiirst one.
    what about the second one??
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    Re: trignometric identities

    Quote Originally Posted by earthboy View Post
    prove that:

    2. \frac{1+\cos A}{\sin A} = \cot (A/2)

    please help...
    Use your double angle identities for sin(A) and cos(A) noting that \cos(A) = \cos \left(2 \cdot \dfrac{A}{2}\right)

    Since you want cot then you want to get cos(A/2) in the numerator rather than sin(A/2)
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    Re: trignometric identities

    Hello, earthboy!

    \text{Prove that: }\:\frac{1+\cos A}{\sin A} \:=\: \cot \frac{A}{2}

    Right side: . \cot\frac{A}{2} \;=\;\frac{\cos\frac{A}{2}}{\sin\frac{A}{2}} \;=\;\frac{\sqrt{\frac{1+\cos A}{2}}}{\sqrt{\frac{1-\cos A}{2}}} \;=\;\sqrt{\frac{1+\cos A}{1-\cos A}}

    Multiply by \tfrac{1+\cos A}{1+\cos A}\!:\;\;\sqrt{\frac{1+\cos A}{1-\cos A}\cdot\frac{1+\cos A}{1+\cos A}} \;=\;\sqrt{\frac{(1+\cos A)^2}{1-\cos^2A}}

    . . . . . . . . . . . . =\;\sqrt{\frac{(1+\cos A)^2}{\sin^2\!A}} \;=\; \frac{1+\cos A}{\sin A}

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