If $ \csc x= \sec 70^{ \circ }$, then solve for $x$.

Remember that cosecant and secant are cofunctions:

$\csc x= \sec (90-x)$.

Set $ \sec (90-x)$ equal to $\sec 70^{\circ}$ to determine $x$.

$90-x=70$.

$x=20^{ \circ }$.

To check your answer, notice $ \csc 20^{ \circ }= \sec (90-20)^{\circ}$.