Chapter 7 - Trigonometric Identities and Equations - 7.1 Fundamental Identities - 7.1 Exercises - Page 659: 74

$\tan ^{4}\theta $

$\dfrac {sec^{2}a-1}{csc^2\theta -1}=\dfrac {\dfrac {1}{\cos ^{2}\theta }-1}{\dfrac {1}{\sin ^{2}\theta }-1}=\dfrac {\dfrac {1-\cos ^{2}\theta }{\cos ^{2}\theta }}{\dfrac {1-\sin ^{2}\theta }{\sin ^{2}\theta }}=\dfrac {\sin ^{4}\theta }{\cos ^{4}\theta }=\tan ^{4}\theta $