let's say that, that equals some angle θ
thus [tex]\bf sec^{-1}(1)=\theta \iff sec(\theta)=1\\\\
-----------------------------\\\\
sec(\theta)=\cfrac{1}{cos(\theta)}\qquad thus\\\\
-----------------------------\\\\
\cfrac{1}{cos(\theta)}=1\implies \cfrac{1}{1}=cos(\theta)\implies 1=cos(\theta)
\\\\\\
\textit{now, taking }cos^{-1}\textit{ to both sides}
\\\\\\
cos^{-1}(1)=\theta[/tex]
so.. .check your Unit Circle, what is that angle anyway?
