Chapter 7 - Trigonometric Identities and Equations - 7.2 Verifying Trigonometric Identities - 7.2 Exercises - Page 667: 69

$\dfrac {\tan ^{2}t-1}{sec^{2}t}=\dfrac {\tan ^{2}t-1}{\tan ^{2}t+1}=\dfrac {\cot t\left( \tan ^{2}t-1\right) }{\cot t\left( \tan ^{2}t+1\right) }=\dfrac {\tan t-\cot t}{\tan t+\cot t}$

$\dfrac {\tan ^{2}t-1}{sec^{2}t}=\dfrac {\tan ^{2}t-1}{\tan ^{2}t+1}=\dfrac {\cot t\left( \tan ^{2}t-1\right) }{\cot t\left( \tan ^{2}t+1\right) }=\dfrac {\tan t-\cot t}{\tan t+\cot t}$