Question

Find tan(x) if sec^2(x) = 3/2?

A. ±√(2)/2
B. ±1/4
C. ±√(6)/2
D. ±1/2

Answer 1

\(\color{#000000 }{ \displaystyle \sec^2x=\tan^2x+1 }\)

\(\color{#000000 }{ \displaystyle \frac{3}{2}=\tan^2x+\frac{2}{2} }\)

\(\color{#000000 }{ \displaystyle \tan^2x=\frac{1}{2} }\)

Answer 2

The first line is a trigonometric identity.

In second line I plug in 3/2 instead of sec²x,
and I re-write 1 as 2/2.

Then I subtract, 2/2 from both sides, and this
way I am able to solve for tan²x.

Answer 3

Now, you need to find tan(x), based on this.

Answer 4

Thank you good sir! This is very thorough response :)

Answer 5

You welcome!