prove. (sinA + cosecA)^2 + (cosA + secA)^2 = 7 + ^2A + ^2A - Vidyadip

Question

prove.
$(sinA + cosecA)^2 + (cosA + secA)^2 = 7 + \tan^2A + \cot^2A$

✓

Answer

$LHS =(sinA + cosecA)^2 + (cosA + secA)^2$
$= \sin^2A + cosec^2A + 2 sinA\ cosecA + \cos^2A + sec^2A + 2 cosA secA$
$= \sin^2A + \cos^2A +cosec^2A +sec^2A + 2 + 2$
$= 1 +cosec^2A +sec^2A + 4$
$= (1 + \cot^2A) + (1 + \tan^2A) + 5$
$= 7 + \tan^2A + \cot^2A = RHS$

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