(C) Let $f(x) = \sqrt{3} \sin x + \cos x$.We can write this as $f(x) = 2 \left( \frac{\sqrt{3}}{2} \sin x + \frac{1}{2} \cos x \right)$.Using the iden

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(C) Let $f(x) = \sqrt{3} \sin x + \cos x$.We can write this as $f(x) = 2 \left( \frac{\sqrt{3}}{2} \sin x + \frac{1}{2} \cos x \right)$.Using the identity $\sin(A + B) = \sin A \cos B + \cos A \sin B$,we have $f(x) = 2 \sin(x + 30^\circ)$.The maximum value of $\sin \theta$ is $1$,which occurs when $\theta = 90^\circ$.Therefore,$x + 30^\circ = 90^\circ$.$x = 90^\circ - 30^\circ = 60^\circ$.

Class 11 Mathematics Trigonometric Functions Maximum and minimum values of trigonometrical functions, Conditional trigonometrical identities

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

A
$30$
B
$45$
C
$60$
D
$90$

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Trigonometric Functions

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Maximum and minimum values of trigonometrical functions, Conditional trigonometrical identities

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

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