Question

Prove the following:

`sinx tan(x/2) + 2cosx = 2/(1 + tan^2(x/2))`

Answer 1

L.H.S. = `sinx tan(x/2) + 2cosx`

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

= `2sin^2  x/2 + 2cosx`

= 1 – cos x + 2cosx

= 1 + cos x

= `2cos^2  x/2`

= `2/(sec^2  x/2)`

= `2/(1 + tan^2  x/2)`

= R.H.S.