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Sin 3 x + Sin 2x - Sin x

= (Sin 3x - Sin x) + Sin 2 x ,; Sin A- Sin B = 2 Sin (A-B)/2 Cos (A+B)/2

= 2 Sin x Cos 2x + 2 Sin x Cos x ; ; Sin 2 A = 2 Sin A Cos A

= 2 Sin x [ Cos 2x + Cos x ] ;; Cos A + Cos B = 2 Cos (A+B)/2 Cos (A-B)/2

= 2 Sin x * 2 Cos 3x/2 Cos x/2

= 4 Sin x * Cos x/2 * Cos 3x/2 = RHS

= (Sin 3x - Sin x) + Sin 2 x ,; Sin A- Sin B = 2 Sin (A-B)/2 Cos (A+B)/2

= 2 Sin x Cos 2x + 2 Sin x Cos x ; ; Sin 2 A = 2 Sin A Cos A

= 2 Sin x [ Cos 2x + Cos x ] ;; Cos A + Cos B = 2 Cos (A+B)/2 Cos (A-B)/2

= 2 Sin x * 2 Cos 3x/2 Cos x/2

= 4 Sin x * Cos x/2 * Cos 3x/2 = RHS