Answer
False
Work Step by Step
We know that a function$ f$ is said to be one-one if $f(x_1)=f(x_2)⇒x_1=x_2 $, in other words if $x_1≠x_2⇒f(x_1)≠f(x_2)$
Also ,We know that
\[\cos (−x)=\cos x\]
For all real x
Here\[ \cos\left(\frac{-π}{2}\right)=
\cos\left(\frac{π}{2}\right)\]
But\[ \left(\frac{-π}{2}\right)\neq
\left(\frac{π}{2}\right)\]
By definition of one-one function
$\Rightarrow $ That's why $\cos x$ is not one-one in $\left[\frac{-π}{2},\frac{π}{2}\right]$
However $\cos x$ is one-one in $\left(\frac{-π}{2},\frac{π}{2}\right)$
