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