Given:
[tex]\frac{cosusecu}{tanu}[/tex]
To simplify and write the given trigonometric expression in terms of sine and cosine, we first note below basic trigonometric identities:
[tex]secu=\frac{1}{cosu}[/tex][tex]tanu=\frac{sinu}{cosu}[/tex]
Next, we plug in what we know:
[tex]\begin{gathered} \frac{cosusecu}{tanu}=\frac{cosu(\frac{1}{cosu})}{\frac{sinu}{cosu}} \\ Simplify\text{ and rearrange} \\ \frac{cosusecu}{tanu}=\frac{cosu}{sinu} \end{gathered}[/tex]
Therefore, the answers are:
[tex]\begin{gathered} f(u)=cosu \\ g(u)=sinu \end{gathered}[/tex]
