Find the Exact Value sec((3pi)/2)^2-tan((3pi)/2)^2

$\sec^{2} (\frac{3 π}{2}) - \tan^{2} (\frac{3 π}{2})$

Rewrite $\sec (\frac{3 π}{2})$ in terms of sines and cosines.

${(\frac{1}{\cos (\frac{3 π}{2})})}^{2} - \tan^{2} (\frac{3 π}{2})$

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

${(\frac{1}{\cos (\frac{π}{2})})}^{2} - \tan^{2} (\frac{3 π}{2})$

The exact value of $\cos (\frac{π}{2})$ is $0$ .

${(\frac{1}{0})}^{2} - \tan^{2} (\frac{3 π}{2})$

The expression contains a division by $0$ . The expression is undefined.

Undefined