Question

If A+B+C=180 degrees, Sin(2A)+sin(2B)+sin(2C)=4sin(A)sin(B)sin(C)

Answer 1

left hand side (LHS) = 2 sin A. cos A + 2 sin (B+C). cos (B - C)

Answer 2

=> 2 sin A. cos A + 2 sin (180 - A).cos ( B - C )

Answer 3

=> 2 sin A. cos A + 2 sin A. cos ( B - C )

Answer 4

=> 2 sin A [ cos A + cos ( B- C ) ]

Answer 5

( but cos A = cos { 180 - ( B + C ) } = - cos ( B + C )

Answer 6

=> 2 sin A [ 2 sin B. sin C ]

=> 4. sin A. sin B. sin C

Answer 7

Do you know what identity formula this is using?