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Sin 4A = 4 cos^3 A sin A - 4 sin^3 A cos...

` Sin 4A = 4 cos^3 A sin A - 4 sin^3 A cos A`

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`L.H.S. = sin4A = sin(3A+A)`
`= sin3AcosA+cos3AsinA`
`=(3sinA-4sin^3A)cosA+(4cos^3A-3cosA)sinA`
`=3sinAcosA-4sin^3AcosA+4cos^3AsinA-3cosAsinA`
`=4cos^3AsinA - 4sin^3AcosA = R.H.S.`
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