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Prove that $\sqrt{\sec^2\theta + \cosec^2 \theta} = \tan \theta + \cot \theta$.
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$$\begin{aligned}& L.H.S = \sqrt{\sec^2\theta + \cosec^2\theta} \\ & = \sqrt{1 + \tan^2\theta + 1 + \cot^2\theta} \\ & = \sqrt{(\tan\theta + \cot\theta)^2} \\ & = \tan \theta + \cot \theta \\ & = R.H.S\end{aligned}$$