The value of sin theta + cos theta will be gr | vedclass

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(B) Let $f(	heta) = \sin 	heta + \cos 	heta = \sqrt{2} \left( \frac{1}{\sqrt{2}} \sin 	heta + \frac{1}{\sqrt{2}} \cos 	heta ight) = \sqrt{2} \s

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$	heta = 45^o$

Vedclass · Answer

(B) Let $f(	heta) = \sin 	heta + \cos 	heta = \sqrt{2} \left( \frac{1}{\sqrt{2}} \sin 	heta + \frac{1}{\sqrt{2}} \cos 	heta ight) = \sqrt{2} \sin \left( 	heta + \frac{\pi}{4} ight)$.Since the maximum value of $\sin(\alpha)$ is $1$,the function $f(	heta)$ attains its maximum value when $\sin \left( 	heta + \frac{\pi}{4} ight) = 1$.This occurs when $	heta + \frac{\pi}{4} = \frac{\pi}{2}$.Solving for $	heta$,we get $	heta = \frac{\pi}{2} - \frac{\pi}{4} = \frac{\pi}{4}$.Converting to degrees,$	heta = 45^o$.

The value of $\sin \theta + \cos \theta$ will be greatest when

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