Question
Prove. $(cosec\ A + \sin A) (cosec\ A - \sin A) = \cot^2 A + \cos^2 A$
✓
Answer
$ \text{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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