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Prove that sin3x = 3sinx – 4sin3x .

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Prove that sin3x = 3sinx – 4sin3x .

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Best answer

sin 3x = sin(2x + x) 

= sin 2xcosx + cos2x sin x 

= 2sin xcosxcosx + (1 – 2sin2x)sin x 

= 2 sin x(1- sin2 x) + sin x – 2 sin3 x 

= 3sinx - 4sin3x

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