Question

Given that tan^2 e= 3/8 what is the value of sec e? A. +√8/3 B.+ √11/8 C. 11/8 D. 8/3

Answer 1

sec e = √(11/8) ⇒ answer B

Explanation:

* Lets revise some identities in trigonometry

# sin²x + cos²x = 1

- Divide both sides by cos²x

∴ sin²x/cos²x + cos²x/cos²x = 1/cos²x

∵ sinx/cosx = tanx

∴ sin²x/cos²x = tan²x

∵ cos²x/cos²x = 1

∵ 1/cosx = secx

∴ 1/cos²x = sec²x

* Now lets write the new identity

# tan²x + 1 = sec²x

- Let x = e

∴ tan²e + 1 = sec²e

- Substitute the value of tan²e in the identity

∵ tan²e = 3/8

∴ 3/8 + 1 = sec²e

- Change the 1 to the fraction 8/8

∴ 3/8 + 8/8 = sec²e ⇒ add the fractions

∴ 11/8 = sec²e

- Take square root for the two sides to find sec e

∴ sec e = √(11/8)

∴ The answer is B

Answer 2

`{ \sec}(e) = \pm \: \sqrt{(11)/(8) }`

EXPLANATION

We use the Pythagorean Identity,

`{ \sec}^(2) (e) = 1 + { \tan}^(2) (e)`

It was given that,

`{ \tan}^(2) (e) = (3)/(8)`

We substitute the values into the identity to obtain,

`{ \sec}^(2) (e) = 1 + (3)/(8)`

`{ \sec}^(2) (e) = (11)/(8)`

We take square root of both sides to get,

`{ \sec}(e) = \pm \: \sqrt{(11)/(8) }`