Maximum value of f(x) = sin x + cos x is | vedclass

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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

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$\sqrt{2}$

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(D) The given function is $f(x) = \sin x + \cos x$.We can rewrite this as $f(x) = \sqrt{2} \left( \frac{1}{\sqrt{2}} \sin x + \frac{1}{\sqrt{2}} \cos x ight)$.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 $\sin 	heta$ is $1$,the maximum value of $f(x)$ is $\sqrt{2} 	imes 1 = \sqrt{2}$.

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

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