(C) The expression is of the form $A \cos \theta + B \sin \theta$,where $\theta = x + \frac{\pi}{3}$,$A = 1$,and $B = 2 \sqrt{2}$.The range of $A \cos

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(C) The expression is of the form $A \cos \theta + B \sin \theta$,where $\theta = x + \frac{\pi}{3}$,$A = 1$,and $B = 2 \sqrt{2}$.The range of $A \cos \theta + B \sin \theta$ is $[-\sqrt{A^2 + B^2}, \sqrt{A^2 + B^2}]$.Here,$A^2 + B^2 = (1)^2 + (2 \sqrt{2})^2 = 1 + 8 = 9$.Thus,$\sqrt{A^2 + B^2} = \sqrt{9} = 3$.The minimum value is $-3$ and the maximum value is $3$.Therefore,the correct option is $C$.

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

Medium

The minimum and maximum values of $\cos \left(x+\frac{\pi}{3}\right)+2 \sqrt{2} \sin \left(x+\frac{\pi}{3}\right)$ are respectively

AP EAMCET 2020 All AP EAMCET

A
$-(2 \sqrt{3}-1)$ and $2 \sqrt{3}-1$
B
$-(1+2 \sqrt{2})$ and $1+2 \sqrt{2}$
C
-$3$ and $3$
D
-$2$ and $2$

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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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