Question

How do you prove the identity `1 / (1- cosx) + 1/ (1+ cosx) = 2 csc^2x`?

Answer 1

Working with the left hand side

`((1+cosx)+(1-cosx))/((1-cosx)(1+cosx))`

`(1+cosx+1-cosx)/(1-cos^2x)`

`2/sin^2x`

`2csc^2x`

which is equal to the right hand side