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Prove the following identities: (sin^2A)...

Prove the following identities: `(sin^2A)/(cos^2A)+(cos^2A)/(sin^2A)=1/(sin^2Acos^2A)-2`

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Given
L.H.S
`(sin^2A)/(cos^2A)+(cos^2A)/(sin^2A)`
=`(sin^4A+cos^4A)/(sin^2Acos^2A)`
=`((sin^2A)^2+(cos^2A)^2)/(sin^2Acos^2A)`
=`((sin^2A+cos^2A)^2-2sin^2Acos^2A)/(sin^2Acos^2A)`
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