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sin 2A + sin 2B + sin 2C = 4 sin A sin B sin C how ???

sin 2A + sin 2B + sin 2C

= 4 sin A sin B sin C 

   how ???

 

Grade:11

1 Answers

Arun
25750 Points
6 years ago
Dear student
 
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
 
Regards
Arun (askIITians forum expert)

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