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Prove that :
$(\sin A + \cosec A)^2 + (\cos A + \sec A)^2 = 7 + \tan^2 A + \cot^2 A$
$(\sin A + \cosec A)^2 + (\cos A + \sec A)^2 = 7 + \tan^2 A + \cot^2 A$
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LHS $= \sin^2A + \cosec^2A + 2 \sin A \cosec A + \cos^2A + \sec^2A + 2 \cos A \sec A$
$= 1 + 1 + \cot^2A + 2 + 1 + \tan^2A + 2$
$= 7 + \tan^2A + \cot^2A = RHS$
$= 1 + 1 + \cot^2A + 2 + 1 + \tan^2A + 2$
$= 7 + \tan^2A + \cot^2A = RHS$