Write 'True' or 'False' and justify your answer. If A+ ^2 A=1, th… - Vidyadip

Question

Write 'True' or 'False' and justify your answer.
If $\cos A+\cos ^2 A=1$, then $\sin ^2 A+\sin ^4 A=1$

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Answer

True.True. $\cos A +\cos ^2 A=1$ [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.

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