Answer
$3$
Work Step by Step
Given: $\cos t=\dfrac{3}{5}$
This implies that
$\sec t=\dfrac{1}{\cos t}=\dfrac{5}{3}$ and
$\sin t=\sqrt {1-\cos^2 t} \implies \sin t=\sqrt {1-(\dfrac{3}{5})^2 }$
or, $\sin t=\dfrac{4}{5}$
As $t$ lies in the first quadrant, thus the value of $\sin t$ will be positive.
Now,
$\tan t+\sec t=\dfrac{\sin t}{\cos t}+\dfrac{5}{3}$
or, $\dfrac{4/5}{3/5}+\dfrac{5}{3}=3$
