Question

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

Answer 1

`2secx.`

Explanation:

The Exp. `=cosx/(1+sinx)+(1+sinx)/cosx`

`={cos^2x+(1+sinx)^2}/{(1+sinx)cosx}`

`=(cos^2x+1+2sinx+sin^2x)/{(1+sinx)cosx}`

`={2(1+sinx)}/{(1+sinx)cosx}....[because, cos^2x+sin^2x=1]`

`=2secx.`