Question

How do you simplify `(sina+tana)/(1+cosa)`?

Answer 1

`(sin(a)+tan(a))/(1+cos(a))=tan(a)`

Explanation:

`(sin(a)+tan(a))/(1+cos(a)) = ((sin(a)+tan(a))(1-cos(a)))/((1+cos(a))(1-cos(a)))`

`=(tan(a)-sin(a)cos(a))/(1-cos^2(a))`

`=(tan(a)-sin(a)cos(a))/sin^2(a)`

`=(cot(a)(tan(a)-sin(a)cos(a)))/(cot(a)sin^2(a))`

`=(1-cos^2(a))/(cos(a)sin(a))`

`=sin^2(a)/(cos(a)sin(a))`

`=sin(a)/cos(a)`

`=tan(a)`