Question

If A, B, C, are the interior angles of a triangle ABC, prove that `tan ((C + A)/2) = cot  B/2`.

Answer 1

We have to prove: `tan((C + A)/2) = cot B/2`

Since we know that in triangle ABC

A + B + C = 180

`=> C + A = 180^@ - B`

`=> (C + A)/2 = 90^@ - B/2`

`=> tan (C + A)/2 = tan (90^@ - B/2)`

`=> tan  (C + A)/2 = cot  B/2`

Proved