Question

if A,B and C are a angles of triangle ABC, then show that tan (A+B/2)=cot c/2

Answer 1

Step-by-step explanation:

$A+B+C=180°$

Divide both by the "2"

$⇒\frac{A+B+C}{2}=\frac{180}{2}$

$⇒\frac{A+B+C}{2}=90$

$⇒\frac{A+B}{2}=90-\frac{C}{2}$

Add the "tan" on both sides

$tan\frac{A+B}{2}=tan(90-\frac{C}{2})$

$tan\frac{A+B}{2}=cot\frac{C}{2}$

HENCE PROVED....