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Prove that: `(sinA+s in3A+sin5A+sin7A)/(cosA+cos3A+cos5A+cos7A)=tan4A`

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Prove that: `(sinA+s in3A+sin5A+sin7A)/(cosA+cos3A+cos5A+cos7A)=tan4A`
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`L.H.S = (sinA+sin3A+sin5A+sin7A)/(cosA+cos3A+cos5A+cos7A)`
`=((sin7A+sinA)+(sin5A+sin3A))/((cos7A+cosA)+(cos5A+cos3A)`
`=((2sin4Acos3A)+(2sin4AcosA))/((2cos4Acos3A+2cos4AcosA))`
`=(2sin4A)/(2cos4A)[(cos3A+cosA)/(cos3A+cosA)]`
`=tan4A = R.H.S.`
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