Question

How do you simplify `tan(theta/2)` using the double angle identities?

Answer 1

`tan(theta/2)=sintheta/(costheta+1)`

Explanation:

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

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

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

= `sintheta/(costheta+1)`