# If sec(t) = 3, how do you find the exact value of csc(90 - t )?

$\sec \left(t\right) = 3$
$\implies \cos \left(t\right) = \frac{1}{3}$
now, we know, $\sin \left(90 - x\right) = \cos x$
$\sin \left(90 - t\right) = \cos \left(t\right) = \frac{1}{3}$
$\csc \left(90 - t\right) = \frac{1}{\sin} \left(90 - t\right) = 3$