Question

2) If A,B and
are interral
angles of a taiangle 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 both sides "tan"

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

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

$Hence$ $proved$