1. 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!

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

Originally Posted by juanma101285
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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1 sin 2a-cos2a/1 sin2a cos2a

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