(D) The given function is $f(x) = \sin x + \cos x$.We can rewrite this as $f(x) = \sqrt{2} \left( \frac{1}{\sqrt{2}} \sin x + \frac{1}{\sqrt{2}} \cos

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(D) The given function is $f(x) = \sin x + \cos x$.We can rewrite this as $f(x) = \sqrt{2} \left( \frac{1}{\sqrt{2}} \sin x + \frac{1}{\sqrt{2}} \cos x \right)$.Using the identity $\sin(x + \frac{\pi}{4}) = \sin x \cos \frac{\pi}{4} + \cos x \sin \frac{\pi}{4}$,we get $f(x) = \sqrt{2} \sin(x + \frac{\pi}{4})$.Since the maximum value of $\sin \theta$ is $1$,the maximum value of $f(x)$ is $\sqrt{2} \times 1 = \sqrt{2}$.

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

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Maximum value of $f(x) = \sin x + \cos x$ is

A
$1$
B
$2$
C
$\frac{1}{\sqrt{2}}$
D
$\sqrt{2}$

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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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Maximum value of $f(x) = \sin x + \cos x$ is

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