Question

If A,B and C are interior angles of a triangleABC then show that tan (A+B/2)=cotc/2​

Answer 1

Step-by-step explanation:

A+B+C=180 (angle sum property in triangle ABC)

A+B=180-C

Divide by 2,

A+B/2=90-C/2

Divide by tan,

tan (A+B)/2=tan(90-C/2)

Therefore, tan(A+B/2)=cot(C/2)       Because,tan(90-theta)=cot(90-theta)