(D) Let $f(x) = \sin(x + \pi/6) + \cos(x + \pi/6)$.Using the identity $\sin \theta + \cos \theta = \sqrt{2} \sin(\theta + \pi/4)$, we have $f(x) = \sq

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(D) Let $f(x) = \sin(x + \pi/6) + \cos(x + \pi/6)$.Using the identity $\sin \theta + \cos \theta = \sqrt{2} \sin(\theta + \pi/4)$, we have $f(x) = \sqrt{2} \sin(x + \pi/6 + \pi/4)$.The maximum value of the sine function is $1$, which occurs when the argument is $\pi/2$.Set $x + \pi/6 + \pi/4 = \pi/2$.$x + 5\pi/12 = \pi/2$.$x = \pi/2 - 5\pi/12 = 6\pi/12 - 5\pi/12 = \pi/12$.

Class 11 Mathematics Trigonometrical Ratios, Functions and Identities Maximum and minimum values of trigonometrical functions, Conditional trigonometrical identities

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The maximum value of $\sin(x + \pi/6) + \cos(x + \pi/6)$ is attained at $x =$

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A
$\pi/2$
B
$\pi/4$
C
$\pi/6$
D
$\pi/12$

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Trigonometrical Ratios, Functions and Identities

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Maximum and minimum values of trigonometrical functions, Conditional trigonometrical identities

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