SOLUTION: Sorry to bother you, but I'm a bit stuck with this proof. "Prove {{{(2tan(A))/(1+tan^2(A))}}} = sin(2A) Any help would be greatly appreciated. Thank you

Algebra ->  Trigonometry-basics -> SOLUTION: Sorry to bother you, but I'm a bit stuck with this proof. "Prove {{{(2tan(A))/(1+tan^2(A))}}} = sin(2A) Any help would be greatly appreciated. Thank you      Log On


   

Question 703932: Sorry to bother you, but I'm a bit stuck with this proof.
"Prove %282tan%28A%29%29%2F%281%2Btan%5E2%28A%29%29 = sin(2A)
Any help would be greatly appreciated.
Thank you
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

%282tan%28A%29%29%2F%281%2Btan%5E2%28A%29%29 = sin(2A)

Work with the left side. Use the identity tan%28theta%29=sin%28theta%29%2Fcos%28theta%29
on the top and use the identity 1%2Btan%5E2%28theta%29=sec%5E2%28theta%29
on the bottom:

%28++2sin%28A%29%2Fcos%28A%29++%29%2F%28sec%5E2%28A%29%29 = 

Use the identity sec%28theta%29=1%2Fcos%28theta%29 on the bottom:

%28++2sin%28A%29%2Fcos%28A%29++%29%2F%28%0D%0A%0D%0A%281%2Fcos%28A%29%29%5E2%0D%0A%0D%0A%29

%28++2sin%28A%29%2Fcos%28A%29++%29%2F%28%0D%0A%0D%0A1%2Fcos%5E2%28A%29%0D%0A%0D%0A%29

Invert and multiply:

%28++2sin%28A%29%2Fcos%28A%29++%29%2A%28%0D%0A%0D%0Acos%5E2%28A%29%2F1%0D%0A%0D%0A%29

Cancel the cosine in the bottom into one of the cosine
factors in the top



2sin(A)cos(A)

We use the identity sin%282theta%29=2sin%28theta%29cos%28theta%29

sin(2A)

Edwin