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Prove that: (sin5A-sin3A)/(cos5A+cos3A)=...

Prove that: `(sin5A-sin3A)/(cos5A+cos3A)=tanA`

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1)`=(sin5A-sin3A)/(cos5A+cos3A)`
`=(2sin((5A-3A)/2)cos((5A+3A)/2))/(2cos((5A+3A)/2)cos((5A-3A)/2)`
`=sinA/cosA`
`=tanA`
RHS
2)`=(sinA+sin3A)/(cosA+cos3A)`
`=(2cos((A-3A)/2)sin((A+3A)/2))/(2cos((A+3A)/2)cos((A-3A)/2)`
`=(2cos(-A)sin2A)/(2cos2Acos(-A)`
...
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