Question

The difference between the greatest and least value of $\cos x+\cos \frac{2x}{2}-\cos \frac{3x}{3}$.

Answer 1

here, we are given,

$\cos x+\cos \frac{2x}{2}-\cos \frac{3x}{3}$

$=\cos x+\cos x-\cos x$

$=\cos x$

So, The Range of $\cos x$ is $[-1,1]$

So, the Maximum value of $\cos x$ is $1$

& the Minimum value of $\cos x$ is $-1$.

So, the difference between the greatest and least value of $\cos x$ is

$=1-(-1)=2$.