Question : If $\sin A+\sin ^2 A=1$, then the value of the expression $\left(\cos ^2 A+\cos ^4 A\right)$ is
Option 1: $\frac{3}{2}$
Option 2: $1$
Option 3: $2$
Option 4: $\frac{1}{2}$
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Correct Answer: $1$
Solution :
Given, $\sin A+\sin ^2 A=1$
$⇒\sin A=1-\sin ^2 A$
$⇒\sin A=\cos ^2 A$
So, $\cos ^2 A+\cos ^4 A= \cos ^2 A+\sin ^2 A=1$ [$\because \cos^2 A + \sin^2A=1$]
Hence, the correct answer is 1.
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