The value of x for the maximum value of sqrt{ | vedclass

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Question

(A) Let $f(x) = \sqrt{3} \cos x + \sin x$.We can rewrite this expression by multiplying and dividing by $2$:$f(x) = 2 \left( \frac{\sqrt{3}}{2} \cos x

Vedclass · Accepted Answer

$30$

Vedclass · Answer

(A) Let $f(x) = \sqrt{3} \cos x + \sin x$.We can rewrite this expression by multiplying and dividing by $2$:$f(x) = 2 \left( \frac{\sqrt{3}}{2} \cos x + \frac{1}{2} \sin x \right)$.Using the identity $\sin(A + B) = \sin A \cos B + \cos A \sin B$,where $\sin 60^\circ = \frac{\sqrt{3}}{2}$ and $\cos 60^\circ = \frac{1}{2}$,we get:$f(x) = 2 \sin(x + 60^\circ)$.The maximum value of the sine function is $1$,which occurs when the angle is $90^\circ$.Therefore,for the maximum value of $f(x)$:$x + 60^\circ = 90^\circ$$x = 90^\circ - 60^\circ = 30^\circ$.

The value of $x$ for the maximum value of $\sqrt{3} \cos x + \sin x$ is .....$^o$

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