Hi, I was solving an integral and got this substitution
t= tg(x/2) then sin(x) = (2t)/(1+t^2) and cos(x) = (1-t^2)/(1+t^2)
How did I get sin(x) = (2t)/(1+t^2)?
I know that t = sinx/(cosx+1) and sinx = [(cosx+1)*t]
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Unfortunately, you start off by saying you "know" something that isn't true! so . We have the trig identities and so , , , so that .
Last edited by HallsofIvy; Jun 18th 2013 at 02:00 PM.
An alternative route through this is to start with the identity
Let and we have
Now draw a right-angled triangle with Use Pythagoras to calculate the hypotenuse and so read off the expressions for
Thank you both, I'll be studying this before my exam.
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