Question

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

Answer 1

Given function is : tan (C + A)/2 = cot B/2

Sum of all the angles of a triangle = 180 degree

So, A + B + C = 180°

Or A + C = 180° – B

And, (A + C)/2 = (180° – B)/2 = 90° – B/2

Now, tan (A + C)/2 = tan(90° – B/2) = cot B/2

Hence Proved.