The minimum value of cos theta + sin theta is | vedclass

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(B) Let $f(	heta) = \cos 	heta + \sin 	heta$.We can rewrite this expression by multiplying and dividing by $\sqrt{2}$:$f(	heta) = \sqrt{2} \left(

Vedclass · Accepted Answer

$-\sqrt{2}$

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(B) Let $f(	heta) = \cos 	heta + \sin 	heta$.We can rewrite this expression by multiplying and dividing by $\sqrt{2}$:$f(	heta) = \sqrt{2} \left( \frac{1}{\sqrt{2}} \cos 	heta + \frac{1}{\sqrt{2}} \sin 	heta ight)$Using the identity $\sin(A+B) = \sin A \cos B + \cos A \sin B$,we get:$f(	heta) = \sqrt{2} \sin \left( 	heta + \frac{\pi}{4} ight)$Since the range of the sine function is $[-1, 1]$,we have:$-1 \le \sin \left( 	heta + \frac{\pi}{4} ight) \le 1$Multiplying by $\sqrt{2}$,we get:$-\sqrt{2} \le \sqrt{2} \sin \left( 	heta + \frac{\pi}{4} ight) \le \sqrt{2}$Therefore,the minimum value of the expression is $-\sqrt{2}$.

The minimum value of $\cos \theta + \sin \theta$ is

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