This can be simplified in different ways one way:

`[(sinAcosB+cosAsinB)(sinAcosB-cosAsinB)]/[cos^2Acos^2B]=`

`[sin^2Acos^2B-cos^2Asin^2B]/[cos^2Acos^2B]=`

`[sin^2Acos^2B]/[cos^2Acos^2B]-[cos^2Asin^2B]/[cos^2Acos^2B]=`

`[sin^2A]/[cos^2A]-[sin^2B]/[cos^2B]=`

`tan^2A-tan^2B`