Question

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

• A. $[2,4]$
• B. $[-1,1]$
• C. $[-2,2]$
• D. $[-\sqrt{2},\sqrt{2}]$

Answer 1

The correct option is D $[-\sqrt{2},\sqrt{2}]$

$f\left(x\right)=\frac{\sqrt{2}}{\sqrt{2}}(\frac{1}{\sqrt{2}}\cos 2x-\frac{1}{\sqrt{2}}\sin 2x)$

$=\sqrt{2}(\sin \pi /4\cos x-\cos \pi /4\sin 2x)$

$=\sqrt{2}\left(\sin \right(\pi /4-2x\left)\right)$

Range of $f\left(x\right)\in [-\sqrt{2},\sqrt{2}]$