The maximum value of 3 sin x + 4 cos x is: | vedclass

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(C) Let $f(x) = a \sin x + b \cos x$. The maximum value of this expression is given by $\sqrt{a^2 + b^2}$.Here,$a = 3$ and $b = 4$.Maximum value $= \s

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(C) Let $f(x) = a \sin x + b \cos x$. The maximum value of this expression is given by $\sqrt{a^2 + b^2}$.Here,$a = 3$ and $b = 4$.Maximum value $= \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$.Alternatively,using derivatives: $f'(x) = 3 \cos x - 4 \sin x$.Setting $f'(x) = 0$ gives $	an x = 3/4$.For $	an x = 3/4$,we have $\sin x = 3/5$ and $\cos x = 4/5$ (in the first quadrant).Substituting these values,$f(x) = 3(3/5) + 4(4/5) = 9/5 + 16/5 = 25/5 = 5$.

The maximum value of $3 \sin x + 4 \cos x$ is:

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