Question

For triangle ABC, show that:

`sin (("A + B")/(2)) = cos  "C"/(2)`

Answer 1

We know that for a triangle ΔABC

A + B + C = 180°

A + B = 180° - C

L.H.S. =  sin `("A"+"B")/2`

= sin `(180-  "C")/2`

= sin `(180/2-"C"/2)`

= sin `(90-"C"/2)`

= cos `("C"/2)`