Question

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

Answer 1

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

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 √(25 - 1) \\ = \pm √(24) \\ \therefore \: \tan \theta = \pm 2√(6) \\ \because \theta \: lies \: in \: the \: first \: quadrant \\ \ \therefore \: \tan \theta = \boxed {2} \sqrt{\boxed{6}}`