SOLUTION: Prove the identity: (1/1-cosx)-(cosx/1+cosx)=2csc^2(x)-1

Question 714587: Prove the identity:
(1/1-cosx)-(cosx/1+cosx)=2csc^2(x)-1
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Prove the identity:
(1/1-cosx)-(cosx/1+cosx)=2csc^2(x)-1
start with left side:
(1/1-cosx)-(cosx/1+cosx)
=1+cosx-cosx(1-cosx)/(1-cosx)(1-cosx)
=1+cosx-cosx+cos^2x/(1-cos^2x)
=1+cos^2x/(1-cos^2x)
=(1+1-sin^2x)/1-(1-sin^2x)
=(2-sin^2x)/sin^2x
=(2/sin^2x)/(-(sin^2x)/(sin^2x))
=2csc^2x-1
verified: left side=right side
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