Question #fa8db

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Answer 1 · 2016-10-21T10:08:51

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$sin (3x)=3sin x-4sin^3 x$

Use the formulas
$sin (A+B) = sin A cos B + cos A sin B$

$sin 2A = 2sin A cos A$

$cos 2A = 1- 2 sin ^ 2 A$

Left Side: $sin 3x=sin(2x+x)=sin2xcosx+cos2xsin x$

$=2sinx cosx cosx + (1-2sin^2 x)sin x$

$=2sinx cos^2 x+ sinx-2sin^3 x$

$=2sinx(1-sin^2 x) + sinx-2 sin^3 x$

$=2 sin x-2sin^3 x + sin x -2 sin^3 x$

$=3 sin x -4 sin^ 3 x$

$=$ Right Side