(D) We know that any function of the form $f(x) = a \cos x + b \sin x$ can be written as $f(x) = \sqrt{a^2 + b^2} \cos(x + \alpha)$,where $\tan \alpha

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(D) We know that any function of the form $f(x) = a \cos x + b \sin x$ can be written as $f(x) = \sqrt{a^2 + b^2} \cos(x + \alpha)$,where $\tan \alpha = \frac{b}{a}$.Here,$a = 1$ and $b = -1$.Thus,$f(x) = \sqrt{1^2 + (-1)^2} \cos(x + \alpha) = \sqrt{2} \cos(x + \alpha)$.Since the range of $\cos(x + \alpha)$ is $[-1, 1]$,the range of $f(x)$ is $[-\sqrt{2}, \sqrt{2}]$.

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

Easy

The range of $f(x) = \cos x - \sin x$ is

A
$(-1, 1)$
B
$[-1, 1)$
C
$[-\frac{\pi}{2}, \frac{\pi}{2}]$
D
$[-\sqrt{2}, \sqrt{2}]$

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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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DifficultTS EAMCET 2025

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DifficultJEE MAIN 2019

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EasyAP EAMCET 2006

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AP EAMCET 2025

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The minimum value of $3 \cos x + 4 \sin x + 5$ is

Easy

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The range of $f(x) = \cos x - \sin x$ is

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If $5 \sin \theta + 3 \cos \left(\theta + \frac{\pi}{3}\right) + 3$ lies between $\alpha$ and $\beta$ (including $\alpha, \beta$ also),then $(\alpha - \beta)(\alpha + \beta - 6) = $

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