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 ???
L.SRILAKSHMI , 8 Years ago
Grade 11
Trigonometry> sin 2A + sin 2B + sin 2C = 4 sin A sin B ...
1 Answers
Arun
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
=> 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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