Question

How do you prove `(1- cosx)/sinx = tan(x/2)`?

Answer 1

See the Proof given in the Explanation Section.

Explanation:

Recall that, #1-cos theta=2sin^2 (theta/2), and, sin theta=2sin(theta/2)cos(theta/2)#.

Using these, we have,

`"The L.H.S.="{cancel2sin^cancel2(x/2)}/(cancel(2sin(x/2))cos(x/2)}`

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

`=tan(x/2)`

`="the R.H.S."`