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Prove that: (cos2A\ cos3A-cos2Acos7A+cos...

Prove that: `(cos2A\ cos3A-cos2Acos7A+cos10 A cos A)/(sin4A\ sin3A-sin2A sin5A+sin4Asin7A )=cot6A\ cot5A`

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Multiply above and below by 2 and apply

`text { LHS } frac{(cos 5 A+cos A)-(cos 9 A+cos 5 A)+(cos 11 A+cos 9 A)}{(cos A+cos 7 A)-(cos 3 A+cos 7 A)+(cos 3 A+cos 11 A)}= `

`frac{(cos A+cos 11 A)}{(cos A-cos 11 A)}=frac{2 cos 6 A cos 5 A}{2 sin 6 A sin 5 A}=cot 6 A cot 5 A`

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