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(sin^2 3A)/(sin^2A)-(cos^2 3A)/(cos^2A)=...

`(sin^2 3A)/(sin^2A)-(cos^2 3A)/(cos^2A)=`

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`(sin^(2)3A)/(sin^(2)A)-(cos^(2)3A)/(cos^(2)A)`
`=(sin^(2)3Acos^(2)A-cos^(2)3Asin^(2)A)/(sin^(2)A cos^(2)A)`
`=(sin^(2)3A(1-sin^(2)A)-cos^(2)3Asin^(2)A)/(sin^(2)A cos^(2)A)`
`=(sin^(2)3A-sin^(2)A(cos^(2)3A+sin^(2)3A))/(sin^(2)Acos^(2)A)`
`=(sin(3A+A)sin(3A-A))/(sin^(2)A cos^(2)A)`
`=(sin(3A+A)sin(3A-A))/(sin^(2)Acos^(2)A)` .
`((4 sin A cos A cos 2A)(2sin A cos A))/(sin^(2)A cos^(2)A)=8cos2A`.
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