Question

if A,B,C is angle of a tranglethen prove that tan(B+C/2)=cotA/2

Answer 1

by angle sum property ,
A+B+C = 180
divide both side by 2
( A+ B + C)/2=180/2
(B+ C)/2=90-A/2
Now, multiply both side by tan
tan ( B+ C)/2=tan (90-A /2)
since, tan(90-A)=cotA
therefore,
tan(B+ C)/2=cot A/2
hence proved....

Answer 2

If, A, B, C are angles of a triangle,
So, A+B+C=180°(Angle sum property of a triangle)
=>A/2+B/2+C/2=180/2
=>B/2+C/2=90°-A/2
=>(B+C)/2=90°-A/2
=>tan(B+C/2)=tan(90°-A/2)(multiplying tan both
=>tan(B+C/2)=cotA/2 the sides)