The identity `(sin theta + tan theta)/(1 + cos theta) = tan theta` has to be verified.

`(sin theta + tan theta)/(1 + cos theta)`

=> `(sin theta + (sin theta)/(cos theta))/(1 + cos theta)`

=> `(sin theta*cos theta + sin theta)/(cos theta*(1 + cos theta))`

=> `(sin theta(1 + cos theta))/(cos theta*(1 + cos theta))`

=> `(sin theta)/(cos theta)`

=> `tan theta`

**This proves: **`(sin theta + tan theta)/(1 + cos theta) = tan theta`