Question

Given that tan^2 0=3/8, what is the value of sec 0?

Answer 1

The value of
`\sec\theta =\pm\sqrt{(11)/(8)}`.

Solution:

Given data:

`$\tan^2\theta=(3)/(8)`

To find the value of
`\sec\theta:`

Using trigonometric identity,

`\sec^2\theta=1+\tan^2\theta`

Substitute
`\tan^2\theta=(3)/(8)` in the identity, we get

`$\Rightarrow \sec^2\theta=1+(3)/(8)`

1 can be written as
`(1)/(1)`.

`$ =(1)/(1) +(3)/(8)`

Do cross multiplication.

`$ =(8)/(8) +(3)/(8)`

Denominators are same, so you can add the fractions.

`$ =(8+3)/(8)`

`$\Rightarrow \sec^2\theta =(11)/(8)`

Taking square root on both sides, we get

`$\Rightarrow \sec\theta =\pm\sqrt{(11)/(8)}`

Option B is the correct answer.

Hence the value of
`\sec\theta =\pm\sqrt{(11)/(8)}`.