Question
Prove. $cosec^4A - cosec^2 A = \cot^4 A + \cot^2 A$
✓
Answer
$ \text{LHS} =cosec^4A - cosec^2 A$
$= cosec^2 A (cosec^2A- 1)$
$RHS = \cot^4A + \cot^2 A$
$= \cot^2 A (\cot^2 A + 1)$
$= (cosec^2 A - 1) \ cosec^2 A$
Thus, $ \text{LHS = LHS}$
$= cosec^2 A (cosec^2A- 1)$
$RHS = \cot^4A + \cot^2 A$
$= \cot^2 A (\cot^2 A + 1)$
$= (cosec^2 A - 1) \ cosec^2 A$
Thus, $ \text{LHS = LHS}$
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