Question

if a b c are the interior angles of triangle then prove that tan(A+B)=Cot C/2​

Answer 1

In triangle sum of interior angles=180⁰

Α+B+C=180⁰

Α+B. =180⁰-C

(A+B)/2=90⁰-C

Taking tangent

tan(A+B)/2=tan(90⁰-C/2)

tan(A+B)/2=Cot(C/2)

    Hence Proved.

Answer 2

Answer:

⇒ (A + B + C) = 180°

⇒ (A + B) = 180˚ – C

⇒ (A + B)/2 = 90˚ – C/2

• Taking tan on both sides, we get

↠ tan (A + B)/2 = tan(90˚ - C/2)

= cot C/2

Hence proved.