(C) Let $f(x) = \sin x + \cos 2x$.Using the identity $\cos 2x = 1 - 2\sin^2 x$,we get:$f(x) = \sin x + 1 - 2\sin^2 x$.Let $t = \sin x$,where $t \in [-

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(C) Let $f(x) = \sin x + \cos 2x$.Using the identity $\cos 2x = 1 - 2\sin^2 x$,we get:$f(x) = \sin x + 1 - 2\sin^2 x$.Let $t = \sin x$,where $t \in [-1, 1]$.Then $f(t) = -2t^2 + t + 1$.This is a downward-opening parabola. The vertex occurs at $t = -b/(2a) = -1/(2 \times -2) = 1/4$.Since $1/4 \in [-1, 1]$,the maximum value is $f(1/4) = -2(1/4)^2 + (1/4) + 1$.$f(1/4) = -2(1/16) + 1/4 + 1 = -1/8 + 2/8 + 8/8 = 9/8$.

Class 11 Mathematics Trigonometrical Ratios, Functions and Identities Maximum and minimum values of trigonometrical functions, Conditional trigonometrical identities

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What is the maximum value of $f(x) = \sin x + \cos 2x$?

A
$0$
B
$-2$
C
$9/8$
D
None of these

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Trigonometrical Ratios, Functions and Identities

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Maximum and minimum values of trigonometrical functions, Conditional trigonometrical identities

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