Answer :
We begin with the definition of the secant function:
[tex]$$
\sec y=\frac{1}{\cos y}.
$$[/tex]
We are given that
[tex]$$
\sec y=\frac{13}{15}.
$$[/tex]
Substituting into the definition, we have
[tex]$$
\frac{13}{15}=\frac{1}{\cos y}.
$$[/tex]
To solve for [tex]$\cos y$[/tex], we take the reciprocal of both sides:
[tex]$$
\cos y=\frac{15}{13}.
$$[/tex]
Thus, the cosine of [tex]$y$[/tex] is
[tex]$$
\cos y=\frac{15}{13}\approx1.153846.
$$[/tex]
[tex]$$
\sec y=\frac{1}{\cos y}.
$$[/tex]
We are given that
[tex]$$
\sec y=\frac{13}{15}.
$$[/tex]
Substituting into the definition, we have
[tex]$$
\frac{13}{15}=\frac{1}{\cos y}.
$$[/tex]
To solve for [tex]$\cos y$[/tex], we take the reciprocal of both sides:
[tex]$$
\cos y=\frac{15}{13}.
$$[/tex]
Thus, the cosine of [tex]$y$[/tex] is
[tex]$$
\cos y=\frac{15}{13}\approx1.153846.
$$[/tex]