Question
Prove.
$(cosec A + \sin A) (cosec A - \sin A) = \cot^2 A + \cos^2 A$
$(cosec A + \sin A) (cosec A - \sin A) = \cot^2 A + \cos^2 A$
✓
Answer
$LHS =(cosec A + \sin A) (cosec A - \sin A)$
$= cosec^2 A - \sin^2 A$
$= (1 + \cot^2 A) - (1 - \cos^2 A)$
$=\cot^2 A + \cos^2 A = RHS$
$= cosec^2 A - \sin^2 A$
$= (1 + \cot^2 A) - (1 - \cos^2 A)$
$=\cot^2 A + \cos^2 A = RHS$
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