3x Prove that sin 3x+sin 2x - sinx = 4sin x cos -cos - 2

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( begin{aligned} L H S=sin 3 x+sin 2 x-sin x &=sin 2 x =&(sin 3 x-sin x)+cos left(frac{3 x+x}{2}right)+2 sin x cos x =& 2 sin left(frac{3 x-x}{2}right) =& 2 sin x cos 2 x+2 sin x cos x =& 2 sin x(cos 2 x+cos x) =& 2 sin xleft(2 cos left(frac{2 x+x}{2}right) cos left(frac{2 x-x}{2}right)right) =& 4 sin x cos frac{x}{2} cos frac{3 x}{2} =& R H S text { Hence, proved. } end{aligned} )

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