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Prove that sin3theta=3sintheta-4sin^3theta

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prove sin (3Ø) = 3sin Ø - 4sin^3 Ø

LS = sin(2Ø + Ø)
= sin2Ø cosØ + cos2ØsinØ
= 2sinØcosØcosØ + (1-2sin^2 Ø)sinØ
= 2sinØ(1-sin^2 Ø) + sinØ - 2sin^3 Ø
= 2sinØ - 2sin^2 Ø + sinØ - 2sin^3 Ø
= 3sinØ - 4sin^2 Ø
= RS

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