Question

In triangle abc prove that tan of A + B by 2 is equals to cot C by 2

Answer 1

In trinagle
A + B + C = 180
SO A+ B = 180 - C
and
By using tan (90- A ) = cot A

Answer 2

A+B+C=180
A+B=180-C
dividing all terms by 2
A+B/2=90-C/2
that is
tan(A+B) =tan(90-C/2)
that is
tan(A+B) =cot C/2