Answer
$0.9916$
Work Step by Step
Given: $\sin t=\dfrac{-8}{17}$
This implies that
$\csc t=\dfrac{1}{\sin t}=-\dfrac{17}{8}$ and
$\cos t=\sqrt {1-\sin^2 t} \implies \cos t=\sqrt {1-(\dfrac{-8}{17})^2 }$
or, $\cos t=\dfrac{15}{17}$
As $t$ lies in the fourth quadrant, thus the value of $\cos$ will be positive.
That is, $\sec t=\dfrac{1}{\cos t}=\dfrac{17}{15}$
Now,
$\csc t+\sec t=-\dfrac{17}{8}+\dfrac{\sqrt {17}}{15}=0.9916$
