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Write sin2x - sin5x as a product of trigonometric function?

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Write sin2x - sin5x as a product of trigonometric function?

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  1. 2x = (2x+5x)/2 + (2x-5x)/2

    5x = (2x+5x)/2 - (2x-5x)/2

    So,

    sin2x - sin5x

    = sin[(2x+5x)/2 + (2x-5x)/2] - sin[ (2x+5x)/2 - (2x-5x)/2 ]

    = - 2cos[7x/2] sin[3x/2]


  2. Sinc -sind=2cos[(c+d)/2]sin[(c-d)/2]

    Hence sin2x-sin5x=2cos[7x/2]sin[-3x/2]

    = -2cos[7x/2]sin[3x/2]
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