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Range of Trigonometric Expressions

The greatest ...

Question

The greatest value of ${sin}^{4} q + {cos}^{4} q$ is

\frac{1}{2}

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3

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1

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Solution

The correct option is C $1$
${sin}^{4} x + {cos}^{4} x$ can be written as $({cos}^{2} x + {sin}^{2} x)^{2} - 2 {sin}^{2} x {cos}^{2} x$
$= 1 - \frac{{sin}^{2} (2 x)}{2}$
So max value can be 1 when $sin (2 x) = 0$
Option D

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