# How do you simplify the expression sec(arctan ((2x)/5))?

Aug 22, 2016

$\sqrt{1 + \frac{4}{15}} {x}^{2}$

#### Explanation:

Let $a = a r c \tan \left(\left(\frac{2}{5}\right) x\right) \in Q 1 \mathmr{and} Q 4$, according as $x > \mathmr{and} < 0$.

Then, $\tan a = \frac{2}{5} x , \mathmr{and} \sec > 0$, in both Q1 and Q4.

Now, the given expression is

$\sec a = \sqrt{1 + {\tan}^{2} a} = \sqrt{1 + \frac{4}{15}} {x}^{2}$.

If a is assumed to be the general value, it might $\in Q 3$, for negative

x. In this case, sec a becomes negative and the answer becomes

$\pm \sqrt{1 + \frac{4}{25} {x}^{2}} ,$..