Chapter 7 - Review Exercises - Page 552: 12

$\frac{sec^2(-θ)}{csc^2~θ}=tan^2θ$

$sec^2(-θ)=sec^2θ$ $sec~θ=\frac{1}{cos~θ}$ $csc~θ=\frac{1}{sin~θ}$ $\frac{sec^2(-θ)}{csc^2~θ}=\frac{\frac{1}{cos^2~θ}}{\frac{1}{sin^2~θ}}=\frac{1}{cos^2θ}\frac{sin^2θ}{1}=\frac{sin^2θ}{cos^2θ}=tan^2θ$