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

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  • 1 decade ago
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    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

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