SOLUTION: Tan 1/2x = Cscx -cotx verify

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Question 1072923: Tan 1/2x = Cscx -cotx verify
Found 2 solutions by josgarithmetic, MaxWong:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Not written well. If you want to verify tan%28%281%2F2%29x%29=csc%28x%29-cot%28x%29, then you eventually want to use another identity (which you can find in a reference) of tan%28theta%2F2%29=%281-cos%28theta%29%29%2Fsin%28theta%29%29.

Start with the right hand side of YOUR identity to be verified. Definitions for cosecant and cotangent give
1%2Fsin%28x%29-cos%28x%29%2Fsin%28x%29

%281-cos%28x%29%29%2Fsin%28x%29

Equal by referenced identity above to
tan%28x%2F2%29

DONE.

Answer by MaxWong(38) About Me  (Show Source):
You can put this solution on YOUR website!
tan(x/2)
= sin(x/2)/cos(x/2)
=(sqrt((1-cos x)/2))/(sqrt((1+cos x)/2)
=sqrt((1-cos x)/(1+cos x))
=sqrt((1-cos x)^2/(1-cos^2 x))
=sqrt((1-cos x)^2/(sin^2 x))
=(1-cos x)/(sin x)
=1/sin x - cos x/sin x
= csc x - cot x