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.

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
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Let w = x/2; then x = 2w
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2tan(w)/(1+tan^2(w)) = sin(2w)
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2tan(w)/sec^2(w) = sin(2w)
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2tan(w) = sec^2(w)*(2sin(w)(cos(w))
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2tan(w) = 2sin(w)/cos(w)
2tan(w) = 2*tan(w)
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The domain is "All Real Numbers" because the left and
the right side are both sin(x)
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Cheers,
Stan H.
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