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sin3x+sin2x-sinx=4sinxcos(x/2)cos(3x/2)...

`sin3x+sin2x-sinx=4sinxcos(x/2)cos(3x/2)`

Text Solution

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LHS `=sin3x+sin2x-sinx`
`=sin3x+2cos(2x+x)/(2)sin(2x-x)/(2)`
`=2sin(3x)/(2)cos(3x)/(2)+2cos(3x)/(2)sinx/2`
`=2cos(3x)/(2) [ sin(3x)/(2)+sinx/2]`
`=2cos(3x)/(2)[2sin((3x)/(2)+x/2)sin(2x-x)/(2)]`
`=2cos(3x)/(2)[sin(3x)/(2)+sinx/2]`
`=2cos(3x)(2)[2sin(2x)/(2)cosx/2]`
`=2cos(3x)/(2)[2sinxcosx/2]`
`=4sinxcosx/2cos(3x)/(2)`= RHS Hence Proved.
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