Question

The range of $f\left(x\right)=\sqrt{(1-cosx)\sqrt{(1-cos)\sqrt{(1-cosx)\sqrt{....\infty }}}}$ is

• A. $[0,1]$
• B. $[0,\frac{1}{2}]$
• C. $[0,2]$
• D. $[\frac{1}{2},1]$

Answer 1

The correct option is C $[0,2]$

$f\left(x\right)=\sqrt{(1-\cos x)\sqrt{(1-\cos x)\sqrt{(1-\cos x)\sqrt{\cdots \infty }}}}=y{y}^2=(1-\cos x)\sqrt{(1-\cos x)\sqrt{(1-\cos x)\sqrt{(1-\cos x)\sqrt{\cdots \infty }}}}{y}^2=(1-\cos x)yy=1-\cos x$

Range is given as $1-[-1,1]=[0,2]$