# 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)   (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.