Question

If ABC are interior angles of a triangle ABC then show that sin (B+C/2)=cosA/2

Answer 1

A+B+C=180

So,

b+c=180-A

b+c/2=90-a/2 ( Dividing the L.H.S and R.H.S by 2)

sin(b+c/2)

= sin ( 90 -a/2) ( Substituting b+c/2 value)

= cos a/2

Hence Proved