SOLUTION: Using the half-angle formula for tan , express the trigomometric function cosx in terms of t when tan(t/2)=t

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Question 1064484: Using the half-angle formula for tan , express the trigomometric function cosx in terms of t when tan(t/2)=t
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
tan%28t%2F2%29=0+%2B-+sqrt%28%281-cos%28t%29%29%2F%281%2Bcos%28t%29%29%29
tan%5E2%28t%2F2%29=%281-cos%28t%29%29%2F%281%2Bcos%28t%29%29
So then(using a substitution A=cos%28t%29 for better readability),
t%5E2=%281-A%29%2F%281%2BA%29
%281%2BA%29t%5E2=1-A
t%5E2%2BAt%5E2=1-A
At%5E2%2BA=1-t%5E2
A%281%2Bt%5E2%29=1-t%5E2
A=%281-t%5E2%29%2F%281%2Bt%5E2%29
highlight%28cos%28t%29=%281-t%5E2%29%2F%281%2Bt%5E2%29%29