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If the expression 4 sin5x * cos3x * cos2x is expressed as the sum of three sines then two of them are sin 4x and sin 10x. The third one is ...

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 LHS =   4 Sin 5x * Cos 3x * Cos 2x
We know  2 Sin A  Cos B = Sin (A+B)  + Sin (A-B)

   2 Sin 5x Cos 2x  = Sin 7x + Sin 3x

LHS  = 2 * Cos 3x  [ sin 7x  + Sin 3x ]
        = 2 Sin 7 x Cos 3 x  +  2 Sin 3 x  Cos 3x
       =  Sin 10 x + Sin 4 x  + Sin 6x
                                 as  2 Sin A  Cos  A    = Sin 2A

Hence, the answer is Sin 6x

3 3 3
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