$\"\"$

The equation is $\"\"$ .

$\"\"$ .

The range of the cosine function is $\"\"$ .

$\"\"$ .

Then $\"\"$

$\"\"$

Therefore the equation $\"\"$ is continuous on $\"\"$ .

$\"\"$

The function is $\"\"$ , $\"\"$ .

Differentiate $\"\"$ on each side with respect to $\"\"$ .

$\"\"$

The derivative of the function $\"\"$ is always positive.

Hence the function $\"\"$ is an increasing function.

Any increasing function crosses the $\"\"$ axis only for one value of $\"\"$ .

Therefore the function $\"\"$ has exactly one root in the interval $\"\"$ .

$\"\"$

The equation $\"\"$ has exactly one root.