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Prove that $\sqrt{\text{sec}^2 A + \text{cosec}^2 A} = \text{tan } A + \text{cot } A$.
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Sol. L.H.S. = $\sqrt{(1 + \text{tan}^2A) + (1 + \text{cot}^2A)}$
$= \sqrt{\text{tan}^2A + \text{cot}^2A + 2}$
$= \sqrt{(\text{tanA} + \text{cotA})^2}$
$= (\text{tanA} + \text{cotA})$ = R.H.S.
$= \sqrt{\text{tan}^2A + \text{cot}^2A + 2}$
$= \sqrt{(\text{tanA} + \text{cotA})^2}$
$= (\text{tanA} + \text{cotA})$ = R.H.S.