Question

How do you find the exact value of `Sec(Arctan (1/2))`?

Answer 1

`2/sqrt 5`

Explanation:

Let a = arc tan (1/2). Then `tan a = 1/2. So, sec a = 2/sqrt 5`, using `sec a = +-sqrt ( 1 + tan^2a)=+-sqrt ( 1+ 1/4) = +-2/sqrt 5`. Here, tan a is positive. So, sec a is positive and `= 2/sqrt 5`

Now, `sec(arc tan (1/2))=sec(arc sec(2/sqrt 5))=2/sqrt5`