Question

Simplify `sin theta / (1+cos theta)` ?

Answer 1

`sin theta/(1+cos theta) = csc theta-cot theta`

Explanation:

I'm not sure what you are wanting, but here's one way to simplify the expression:

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

`color(white)(sin theta/(1+cos theta)) = (sin theta(1-cos theta))/(1-cos^2 theta)`

#color(white)(sin theta/(1+cos theta)) = (sin theta(1-cos theta))/(sin^2 theta)#

`color(white)(sin theta/(1+cos theta)) = (1-cos theta)/sin theta`

`color(white)(sin theta/(1+cos theta)) = 1/sin theta-cos theta/sin theta`

`color(white)(sin theta/(1+cos theta)) = csc theta-cot theta`

Answer 2

`sintheta/(1+costheta)={2sin(theta/2)cos(theta/2)}/(2cos^2(theta/2)`

`=sin(theta/2)/cos(theta/2)=tan(theta/2).`