Question

If `A+B+C=pi`, prove that : `sin (B+C-A) + sin (C+A-B) + sin (A+B-C)=4sinA sinB sinC`

Answer 1

`LHS=sin(A+B+C-2A)+sin(A+B+C-2B)-sin(A+B+C-2C)`
`=sin (pi-2A)+sin(pi-2B)-sin(pi-2C)`
`=sin2A+sin2B-sin2C.`