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]

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