Question

Prove the following:

`(tan(theta/2) + cot(theta/2))/(cot(theta/2) - tan(theta/2))` = secθ

Answer 1

L.H.S. = `(tan(theta/2) + cot(theta/2))/(cot(theta/2) - tan(theta/2))` 

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

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

= `1/costheta`

= sec θ

= R.H.S.