Answer
$1$
Work Step by Step
Given: $\sec t=-5$
This implies that
$\cos t=\dfrac{1}{\sec t}=\dfrac{-1}{5}$ and
$\sin t=\sqrt {1-\cos^2 t} \implies \sin t=\sqrt {1-(\dfrac{-1}{5})^2 }$
or, $\sin t=\dfrac{\sqrt{24}}{5}$
As $t$ lies in the second quadrant, thus the value of $\sin t$ will be positive.
Now,
$\sin^2 t+\cos ^2 t=(\dfrac{\sqrt{24}}{5})^2+(\dfrac{-1}{5})^2$
or, $\dfrac{24+1}{25}=1$
