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

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(B) Let $f(	heta) = \sin 	heta + \cos 	heta$.To find the maximum value,we can rewrite the expression as $f(	heta) = \sqrt{2} \left( \frac{1}{\sqrt

Vedclass · Accepted Answer

$	heta = 45^\circ$

Vedclass · Answer

(B) Let $f(	heta) = \sin 	heta + \cos 	heta$.To find the maximum value,we can rewrite the expression as $f(	heta) = \sqrt{2} \left( \frac{1}{\sqrt{2}} \sin 	heta + \frac{1}{\sqrt{2}} \cos 	heta ight)$.Using the identity $\sin(A+B) = \sin A \cos B + \cos A \sin B$,we get $f(	heta) = \sqrt{2} \sin(	heta + 45^\circ)$.The maximum value of the sine function is $1$,which occurs when the angle is $90^\circ$.Therefore,$\sin(	heta + 45^\circ) = 1$ implies $	heta + 45^\circ = 90^\circ$.Solving for $	heta$,we get $	heta = 90^\circ - 45^\circ = 45^\circ$.

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

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