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Math Help - Show that cot(A)=(1+sin(2A)+cos(2A))/(1+sin(2A)-cos(2A))

  1. #1
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    Show that cot(A)=(1+sin(2A)+cos(2A))/(1+sin(2A)-cos(2A))

    Hi, I have this problem which I don't know how to solve... I know the following identities, but I don't know how to apply them to the problem.

    These are the identities I know:

    cot(A)=1/tan(A)=sin(A)/cos(A)=sin(2A)/cos(2A)+1

    and I also know that sin(2A)=2sin(A)cos(A) and cos(2A)=cos^2(A)-sin^2(A)

    Thanks a lot!
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  2. #2
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    Re: Show that cot(A)=(1+sin(2A)+cos(2A))/(1+sin(2A)-cos(2A))

    Quote Originally Posted by juanma101285 View Post
    Hi, I have this problem which I don't know how to solve... I know the following identities, but I don't know how to apply them to the problem.

    These are the identities I know:

    cot(A)=1/tan(A)=sin(A)/cos(A)=sin(2A)/cos(2A)+1

    and I also know that sin(2A)=2sin(A)cos(A) and cos(2A)=cos^2(A)-sin^2(A)

    Thanks a lot!
    \cot(A) = \dfrac{\cos(A)}{\sin(A)}

    What have you tried?

    Write 1 as \sin^2(A) + \cos^2(A) in numerator and denominator:

    \dfrac{cos^2(A) + sin^2(A) +2sin(A)cos(A) + cos^2(A) - sin^2(A)}{sin^2(A)+cos^2(A)+2sin(A)cos(A) - cos^2(A) + sin^2(A)}

    Cancel, factor and see what happens
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