# verify that (sinθ+tanθ)/(1+cosθ)=tanθ

### 4 Answers | Add Yours

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`

The identity has to be verified.

=>

=>

=>

=>

=>

**This proves: **

L:H:S: = (sinθ+tanθ)/(1+cosθ)

= (sinθ.cosθ+sinθ)/cosθ(1+cosθ)

= sinθ(cosθ+1)/cosθ(cosθ+1)

= sinθ/cosθ

= tanθ

= R:H:S

L:H:S: = (sinθ+tanθ)/(1+cosθ)

= (sinθ.cosθ+sinθ)/cosθ(1+cosθ)

= sinθ(cosθ+1)/cosθ(cosθ+1)

= sinθ/cosθ

= tanθ

= R:H:S