Question

Question #7ce2b

Answer 1

This expression simplifies to `csctheta`.

Explanation:

We put on a common denominator.

`=>(costheta(1 + costheta))/(sintheta(1 + costheta)) + (sintheta(sin theta))/(sintheta(1 + costheta))`

`=>(costheta + cos^2theta + sin^2theta)/(sin theta(1 + costheta))`

We know that `cos^2x + sin^2x = 1`.

`=>(1 + costheta)/(sintheta(1 + costheta)`

`=>1/sintheta`

By the reciprocal identities, `1/sinx = cscx`.

`=>csctheta`

Hopefully this helps!