If $cos A + {cos}^{2} A = 1$ then ${sin}^{2} A + {sin}^{4} A = 1$ .Is it true or false?

True

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False

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Ambiguous

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Data insufficient

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Solution

The correct option is A True
$c o s A + c o s^{2} A = 1$
$c o s A = 1 - c o s^{2} A$
$c o s A = s i n^{2} A$
Hence
$s i n^{4} A + s i n^{2} A$
$c o s^{2} A + c o s A$
$= 1$
Hence True.

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