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Prove that (sinA+sin2A+sin4A+sin5A)/(cos...

Prove that `(sinA+sin2A+sin4A+sin5A)/(cos A+cos2A+cos 4A+cos5A)=tan3A`.

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`(sinA+sin2A+sin4A+sin5A)/(cosA+cos2A+cos4A+cos5A)`
`=((sin5A+sinA)+(sin4A+sin2A))/((cos 5A+cosA)+(cos4A+cos2A))`
`=(2 sin 3Acos 2A+sin3A cosA)/(2cos3Acos 2A+2cos 3A cos A)`
`=(2sin3A(cos 2A+cos))/(2cos3A(cos 2A+cosA))=tan3A`
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