Question

What is tan 0 when sec 0 = 5? (1,0) tan 0 = [?]V[​

Answer 1

Answer:

$\tan \theta = \boxed {2} \sqrt{\boxed{6}}$

Step-by-step explanation:

$\sec \theta = 5 \: \: (given) \\ \because \: \tan^{2} \theta = { \sec}^{2} \theta - 1\\ \therefore \: \tan \theta = \pm \sqrt{{ \sec}^{2} \theta - 1} \\ = \pm \sqrt{{5}^{2} - 1} \\ = \pm \sqrt{25 - 1} \\ = \pm \sqrt{24} \\ \therefore \: \tan \theta = \pm 2\sqrt{6} \\ \because \theta \: lies \: in \: the \: first \: quadrant \\ \ \therefore \: \tan \theta = \boxed {2} \sqrt{\boxed{6}}$