# If sec(t) = 3, how do you find the exact value of tan^2 (t)?

Jan 10, 2016

8

#### Explanation:

${\sin}^{2} t + {\cos}^{2} t = 1$

If we divide this identity by ${\cos}^{2} t$ we get:

${\tan}^{2} t + 1 = {\sec}^{2} t$

If $\sec t = 3$ then:

${\tan}^{2} t + 1 = 9$

${\tan}^{2} t = 8$