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

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Question

(C) The expression is $f(x) = \sqrt{3} \sin x + \cos x$.We can rewrite this by multiplying and dividing by $\sqrt{(\sqrt{3})^2 + 1^2} = \sqrt{3+1} = 2

Vedclass · Accepted Answer

$60$

Vedclass · Answer

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

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

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