What is the maximum value of the function f(x | vedclass

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(B) To find the maximum value of $f(x) = \sin x + \cos x$,we can rewrite the function by multiplying and dividing by $\sqrt{2}$:$f(x) = \sqrt{2} \left

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$\sqrt{2}$

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(B) To find the maximum value of $f(x) = \sin x + \cos x$,we can rewrite the function by multiplying and dividing by $\sqrt{2}$:$f(x) = \sqrt{2} \left( \frac{1}{\sqrt{2}} \sin x + \frac{1}{\sqrt{2}} \cos x ight)$Using the trigonometric identity $\sin(A+B) = \sin A \cos B + \cos A \sin B$,we can write:$f(x) = \sqrt{2} \left( \sin x \cos \frac{\pi}{4} + \cos x \sin \frac{\pi}{4} ight)$$f(x) = \sqrt{2} \sin \left( x + \frac{\pi}{4} ight)$Since the maximum value of the sine function $\sin 	heta$ is $1$,the maximum value of $f(x)$ is $\sqrt{2} 	imes 1 = \sqrt{2}$.

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

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