2 tan theta /(1 + tan^2 theta) = sin 2theta

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Question from Charmaine, a student:

I'm having trouble on where to begin proving identities. I must prove that
2 tan theta /(1 + tan^2 theta) = sin 2theta

Hi Charmaine,

In a problem like this when I don't immediately see something useful I write everything in terms of sines and cosines and then see if I can manipulate both sides to make them equal. In this case replace tan(θ) by sin(θ)/cos(θ) and sin(2θ) by 2 sin(θ) cos(θ).

Penny

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