SOLUTION: Can someone help me?
How to prove the identity and identify the domain?
(2*tan((1/2)x))/(1+tan^2((1/2)x)=sinx
Thank you.
Algebra ->
Trigonometry-basics
-> SOLUTION: Can someone help me?
How to prove the identity and identify the domain?
(2*tan((1/2)x))/(1+tan^2((1/2)x)=sinx
Thank you.
Log On
Question 1107159: Can someone help me?
How to prove the identity and identify the domain?
(2*tan((1/2)x))/(1+tan^2((1/2)x)=sinx
Thank you. Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! How to prove the identity and identify the domain?
(2*tan((1/2)x))/(1+tan^2((1/2)x)=sinx
-----
Let w = x/2; then x = 2w
-----
2tan(w)/(1+tan^2(w)) = sin(2w)
-----
2tan(w)/sec^2(w) = sin(2w)
----
2tan(w) = sec^2(w)*(2sin(w)(cos(w))
----
2tan(w) = 2sin(w)/cos(w)
2tan(w) = 2*tan(w)
----------------------
The domain is "All Real Numbers" because the left and
the right side are both sin(x)
-------------
Cheers,
Stan H.
------------
(