Question

Prove that `sqrt((1+sinx)/(1-sinx))=tan(pi/4+x/2)`?

Answer 1

Please se below.

Explanation:

`sqrt((1+sinx)/(1-sinx))`

= `sqrt((cos^2(x/2)+sin^2(x/2)+2sin(x/2)cos(x/2))/((cos^2(x/2)+sin^2(x/2)-2sin(x/2)cos(x/2)))`

= `(cos(x/2)+sin(x/2))/(cos(x/2)-sin(x/2))`

= `(1+tan(x/2))/(1-tan(x/2))`

= `(tan(pi/4)+tan(x/2))/(1-tan(pi/4)tan(x/2))`

= `tan(pi/4+x/2)`