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Prove that (sin5x-2sin3x+sinx)/(cos5x-co...

Prove that `(sin5x-2sin3x+sinx)/(cos5x-cosx)=tanx`

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LHS `=(sin5x-2sin3x+sinx)/(cos5x-cosx)`
`=(sin5x+sinx-2sin3x)/(cos5x-cosx)`
`=(2sin3x. Cos2x-2sin3x)/(-2sin3x.sin2x)`
`=(-2sin3x(1-cos2x))/(-2sin3x.sin2x)`
`(1-cos2x)/(sin2x)=(2sin^(2)x)/(2sinxcosx)`
`=(sinx)/(cosx)=tanx` = RHS Hence Proved.
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