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Prove that sin4A=4sinAcos^3A-4sin^3A...

Prove that `sin4A=4sinAcos^3A-4sin^3A`

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`" "`LHS = `sin4A` ltbgt ` " "=2sin2A*cos2A`
`" "=2(2sinA*cosA)(cos^(2)A-sin^(2)A)`
`" "=4sinA*cos^(3)A-4cosAsin^(3)A" "[because cos2A=cos^(2) A -sin^(2) A and sin2A = 2sinA* cosA]`
`therefore" "LHS=RHS" "` Hence proved.
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