The range of f(x) = cos 2x - sin 2x contains | vedclass

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

Question

(B) Given function is $f(x) = \cos 2x - \sin 2x$.We can rewrite this as $f(x) = \sqrt{2} \left( \frac{1}{\sqrt{2}} \cos 2x - \frac{1}{\sqrt{2}} \sin 2

Vedclass · Accepted Answer

$[-1, 1]$

Vedclass · Answer

(B) Given function is $f(x) = \cos 2x - \sin 2x$.We can rewrite this as $f(x) = \sqrt{2} \left( \frac{1}{\sqrt{2}} \cos 2x - \frac{1}{\sqrt{2}} \sin 2x ight)$.Using the identity $\cos(A + B) = \cos A \cos B - \sin A \sin B$,we get $f(x) = \sqrt{2} \cos(2x + \frac{\pi}{4})$.Since the range of $\cos 	heta$ is $[-1, 1]$,the range of $f(x)$ is $[-\sqrt{2}, \sqrt{2}]$.Since $\sqrt{2} \approx 1.414$,the interval $[-\sqrt{2}, \sqrt{2}]$ is approximately $[-1.414, 1.414]$.The set $[-1, 1]$ is a subset of $[-1.414, 1.414]$.Therefore,the range of $f(x)$ contains the set $[-1, 1]$.

The range of $f(x) = \cos 2x - \sin 2x$ contains the set

Similar Questions

If $n(A) = 4$,$n(B) = 3$,and $n(A \times B \times C) = 24$,then $n(C) = $

Let $n(U) = 700, n(A) = 200, n(B) = 300$ and $n(A \cap B) = 100,$ then $n(A^c \cap B^c) = $

Which of the following pairs of sets are not equal?

Find the power set of $A = \{\{a, b\}, c\}$.

If $A = \{a, b\}$,$B = \{2, 3, 5, 6, 7\}$ and $C = \{5, 6, 7, 8, 9\}$,find $A \times (B \cap C)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module