\(\dfrac{\sin^2a-\tan^2a}{\cos^2a-\cot^2a}=\dfrac{\sin^2a-\dfrac{\sin^2a}{\cos^2a}}{\cos^2a-\dfrac{\cos^2a}{\sin^2a}}=\dfrac{\dfrac{\sin^2a\cos^2a-\sin^2a}{\cos^2a}}{\dfrac{\cos^2a\sin^2a-\cos^2a}{\sin^2a}}=\dfrac{\sin^2a\sin^2a\left(\cos^2a-1\right)}{\cos^2a\cos^2a\left(\sin^2a-1\right)}\)
\(=\dfrac{\sin^4a\left(\cos^2a-\cos^2a-\sin^2a\right)}{\cos^4a\left(\sin^2a-\cos^2a-\sin^2a\right)}=\dfrac{\sin^4a\left(-\sin^2a\right)}{\cos^4a\left(-\cos^2a\right)}\)
\(=\dfrac{-\sin^6a}{-\cos^6a}=\dfrac{\sin^6a}{\cos^6a}=\tan^6a\)
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