Question

If A, B and C are interior angles of ∆ABC, then show that : tan(angle A+Angle B/2)=cot angleC/2

Answer 1

Hi there,

A + B + C = 180°

A + B = 180°- C

Put A + B = 180°- C

tan( A + C/2)

tan(180°-C/2)

tan(90°- c/2) = Cot ( 90 - (90°-c/2) 【tan(90°- a) = cota 】

Cot c/2

Hence proved.

Thanks ♥️

Answer 2

accor to angle sum property ,
A+B+C=180
divide by 2 on both the sides
(A+B+C)÷2=180÷2=90
(A+B)÷2=90-(C÷2)
multiply by tan on both the sides
tan(A+B)÷2=tan(90-(C÷2))
=cot(C÷2) {since cot(theta)=tan(90-theta)}

Hence Proved