If cos x + {cos ^2}x = 1, then value of {sin ^2}x + {sin ^4}x is

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3.Trigonometrical Ratios, Functions and Identities

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If $\cos x + {\cos ^2}x = 1,$ then the value of ${\sin ^2}x + {\sin ^4}x$ is

A

$1$

B

$-1$

C

$0$

D

$2$

Solution

(a) $\cos x + {\cos ^2}x = 1\,\,$

$\Rightarrow \,\,\cos x = {\sin ^2}x$

$\therefore \,\,{\sin ^2}x + {\sin ^4}x = \cos x + {\cos ^2}x = 1$.

Standard 11

Mathematics

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