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If $\tan A + \cot A = 6$, then find the value of $\tan^2 A + \cot^2 A-4$.
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Sol. $$\begin{aligned}& (\tan A + \cot A)^2 = 36 \\ & \tan^2 A + \cot^2 A + 2\tan A \cot A = 36 \\ & \tan^2 A + \cot^2 A = 34 \\ & \therefore \tan^2 A + \cot^2 A - 4 = 30\end{aligned}$$