The maximum value of $sin x + cos 2 x$ is -

0

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- 2

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9 / 8

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none of these

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Solution

The correct option is C $9 / 8$
Given, $y = sin x + cos 2 x$
$y = sin x + 1 - 2 {sin}^{2} x$
$y = - 2 {sin}^{2} x + sin x + 1$
It is quadratic equation with $a = - 2, b = 1, c = 1$
So, Maximum value $(4 a c - b^{2}) / 4 a$
$= 9 / 8$

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