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Question

Prove that: sin3x+sin2xsinx=4sinxcosx2,cos3x2.

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Solution

sin3x+sin2xsinx
sinx+si2xsinx
sinxsiny=2cosx+y2sinxy2
sin3x+(sin2xsinx)
sin3x+[2cos(3x2)sinx2]
divide by x2
sin2x2=2sinx2.cosx2
sinx=2sinx2cosx2
sin3x=2sin3y2cos3y2
=2sin3x2cos3x2+[2cos3x2sinx2]
2cos3x2[sin3x2+sinx2]
x=3y2 & y=x2
Wegel,
2cos3x2⎢ ⎢ ⎢ ⎢2sin(4x2)2cos(2x2)2⎥ ⎥ ⎥ ⎥
4cos3x2sinxcosx2
Hence proved

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