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# If $\sin x+\sin^2x=1$ then value of $\cos^2x+\cos^4x$ is equal to

$(a)\;1\qquad(b)\;2\qquad(c)\;1.5\qquad(d)\;None\;of\;these$

$\sin x+\sin^2x=1$
$\Rightarrow \sin x=1-\sin^2x$
$\sin x=\cos^2x$
$\Rightarrow \sin^2x=\cos^4x$
$\sin^2x+\cos^2x=1$
$1-\cos^2x=\cos^4x$
$\Rightarrow \cos^2x+\cos^4x=1$
Hence (a) is the correct answer.