If A + B + C = 180 degree then prove that (sin 2A + sin 2B + sin 2C) = 4 sinA.sinB.sinC ???

Question

80/1

Answer 1

Favorite Answer

Left Hand Side (LHS) = 2 sin A. cos A + 2 sin (B+C). cos (B - C)

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

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

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

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

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

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

PKT