SOLUTION: verify the identity csc(x)-cot(x)= (2(1-cos(x))(1+cos(x)))/(2sin(x)+sin(2x)) by beginning with the known identity that tan(x/2)=tan(x/2).

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Question 26174: verify the identity csc(x)-cot(x)= (2(1-cos(x))(1+cos(x)))/(2sin(x)+sin(2x)) by beginning with the known identity that tan(x/2)=tan(x/2).
Answer by stanbon(57379) About Me  (Show Source):
You can put this solution on YOUR website!
There are many ways to verify identities. One way is to change what you can to sine and cosine expressions.
Left side work:
(1/sinx)-(cosx/sinx)=[1-cosx]/sinx
Right side work:
[2(1-cosx)(1+cosx)[/[2sinx+2sinx cosx]=2(1-cosx)(1+cosx)/2sinx(1+cosx)
=(1-cosx)/sinx
Right side equals left side. This verifies the identity.
Cheers,
Stan H.