Question

How do you perform addition or subtraction and use the fundamental identities to simplify `1/(1+cosx)+1/(1-cosx)`?

Answer 1

`1/(1+cosx)+1/(1-cosx)=2csc^2x`

Explanation:

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

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

= `2/(1-cos^2x)`

= `2/sin^2x`

= `2csc^2x`