Question

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

Answer 1

The value of $\sec\theta =\pm\sqrt{\frac{11}{8}}$.

Solution:

Given data:

$\tan^2\theta=\frac{3}{8}$

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

Using trigonometric identity,

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

Substitute $\tan^2\theta=\frac{3}{8}$ in the identity, we get

$\Rightarrow \sec^2\theta=1+\frac{3}{8}$

1 can be written as $\frac{1}{1}$.

             $=\frac{1}{1} +\frac{3}{8}$

Do cross multiplication.

            $=\frac{8}{8} +\frac{3}{8}$

Denominators are same, so you can add the fractions.

            $=\frac{8+3}{8}$

$\Rightarrow \sec^2\theta =\frac{11}{8}$

Taking square root on both sides, we get

$\Rightarrow \sec\theta =\pm\sqrt{\frac{11}{8}}$

Option B is the correct answer.

Hence the value of $\sec\theta =\pm\sqrt{\frac{11}{8}}$.