First slide

Trigonometric equations

Question

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

Moderate

A

1
B

2
C

more than two
D

0

Solution

Given equation is possible if $\cos (π \sqrt{x - 4}) = 1$ and $\cos (π \sqrt{x}) = 1$ .
Since $x - 4 \geq 0 \Rightarrow x \geq 4$ and $x \geq 0$
So $x = 4$ is the only solution.

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