(Q17)If A,B and C are interior angles of triangle ABC ,then show that tan
A+B
2
=cot
C
2

Answer:

Given A, B and C are interior angles of right angle triangle ABC then A + B + C =°

On dividing the above equation by '2' on both sides,we get °

A+B
2
 +
C
2
 =
°
2
 =°
A+B
2
 =° -
C
2

on taking tan ratio on both sides

tan
A+B
2
 =[tan °-
c
2
]
tan
A+B
2
=cot
C
2

Hence proved