Question
Prove. $ 2 \sin^2A + \cos^4A = 1 + \sin^4A$
✓
Answer
$ \text{LHS} =2 \sin^2A + \cos^4A$
$= 2 \sin^2A + (1 - \sin^2A)^2$
$= 2 \sin^2A + 1 + \sin^4A - 2 \sin^2A$
$= 1 + \sin^4A = RHS$
$= 2 \sin^2A + (1 - \sin^2A)^2$
$= 2 \sin^2A + 1 + \sin^4A - 2 \sin^2A$
$= 1 + \sin^4A = RHS$
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