Verify the identity. cos(x)/(1+sin(x))+(1+sin(x))/cos(x) =2sec(x)

The identity we want to verify is:

.

Note that sec(x)=1/cosx, so we write the right hand side as 2/(cos(x)).

We multiply the first expression by (cosx)/(cosx), and the remaining two by (1+sinx)/(1+sinx) to have them in common numerators:

.

Now we can only consider the numerators. The right hand side, expanding (1+sinx)^2 becomes:

.

From the identity , the expression further simplifies to:

. This proves the identity.