Question

The number of solutions of the equation $cos\left(\pi \sqrt{x-4}\right)cos\left(\pi \sqrt{x}\right)=1$ is

• A. zero
• B. 1
• C. 2
• D. Infinite

Answer 1

The correct option is A zero

Given that,

$\cos \left(\pi \sqrt{x-4}\right)\cos \left(\pi \sqrt{x}\right)=1$

$\cos \left(\pi \sqrt{x-4}\right)\cos \left(\pi \sqrt{x}\right)=\cos 0\times \cos 0$

$\Rightarrow \cos \left(\pi \sqrt{x}\right)=cos0$

$\Rightarrow \pi \sqrt{x}=0$

$\therefore x=0$

$\therefore$ Option (A) is correct answer.