(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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(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 Trigonometric Functions 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
$[-\sqrt{2}, \sqrt{2}]$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Trigonometric Functions

Subtopic

Maximum and minimum values of trigonometrical functions, Conditional trigonometrical identities

If $A+B+C=270^{\circ}$,then $\cos 2A + \cos 2B + \cos 2C + 4 \sin A \sin B \sin C =$

MediumTS EAMCET 2019

View Solution

The number of integral values of $k$ for which the equation $7 \cos x + 5 \sin x = 2k + 1$ has a solution is:

EasyTS EAMCET 2019

View Solution

The maximum value of $\sin(\cos(\tan x))$ is

View Solution

The expression $sin^{2n}x + cos^{2n}x$ lies between which of the following values?

View Solution

The maximum value of the function $f(x) = 3 \sin x + 4 \cos x$ is

Easy

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

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

Similar Questions

If $A+B+C=270^{\circ}$,then $\cos 2A + \cos 2B + \cos 2C + 4 \sin A \sin B \sin C =$

The number of integral values of $k$ for which the equation $7 \cos x + 5 \sin x = 2k + 1$ has a solution is:

The maximum value of $\sin(\cos(\tan x))$ is

The expression $sin^{2n}x + cos^{2n}x$ lies between which of the following values?

The maximum value of the function $f(x) = 3 \sin x + 4 \cos x$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module