1/1-cosx+1/1+cosx=2csc^2x

Prove the Trigonometic identity

secx-tanxsinx=1/secx

Directions ask to prove the identity

tan^2x-sin^2x=tan^2xsin^2x

The directions say to prove the identity. I understand how these two functions work, but I don't understand how to go through the process of getting from the left side to the right side. 

1/x-1/2=2-x/2x

Directions say to prove the algebraic identity by starting with the Left hand side expression and supplying a sequence of equivalent expressions that ends with the right hand expressions

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