Question
Write ‘True’ or ‘False’ and justify your answer.
If $cosA + cos^2A = 1, then sin^2A + sin^4A = 1$
If $cosA + cos^2A = 1, then sin^2A + sin^4A = 1$
✓
Answer
True.$cosA + cos^2A = 1 [Given]$
$\Rightarrow cosA = 1 - cos^2A$
$\Rightarrow cosA = sin^2A$
$\Rightarrow cos^2A = sin^4A$
$Now, LHS = sin^2A + sin^4A$
$= cosA + cos^2A$
$= 1 = RHS$
Hence, the given statement is true.
$\Rightarrow cosA = 1 - cos^2A$
$\Rightarrow cosA = sin^2A$
$\Rightarrow cos^2A = sin^4A$
$Now, LHS = sin^2A + sin^4A$
$= cosA + cos^2A$
$= 1 = RHS$
Hence, the given statement is true.
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