Simplify the express: $\sec \left( \tan ^ { - 1 } x \right)$ .
A)1
B) $x ^ { 2 }$
C) $\sqrt { x }$
D) $\sqrt { x ^ { 2 } + 1 }$
E) $\frac { 1 } { x }$
F) $\frac { 1 } { \sqrt { x ^ { 2 } + 1 } }$
G) $\frac { x } { \sqrt { x ^ { 2 } + 1 } }$
H)
$\frac { \sqrt { x ^ { 2 } + 1 } } { x }$

Question

Simplify the express: $\sec \left( \tan ^ { - 1 } x \right)$ .
A)1
B) $x ^ { 2 }$ 
C) $\sqrt { x }$ 
D) $\sqrt { x ^ { 2 } + 1 }$ 
E) $\frac { 1 } { x }$ 
F) $\frac { 1 } { \sqrt { x ^ { 2 } + 1 } }$
G) $\frac { x } { \sqrt { x ^ { 2 } + 1 } }$ 
H)
$\frac { \sqrt { x ^ { 2 } + 1 } } { x }$

Quizplus · Accepted Answer

To simplify $\sec(\tan^{-1}(x))$, consider a right triangle where the opposite side over the adjacent side (the definition of tangent) equals $x$. If we let the opposite side be $x$ and the adjacent side be $1$, then the hypotenuse, using the Pythagorean theorem, is $\sqrt{x^2 + 1}$. Since $\sec$ is the reciprocal of $\cos$, and $\cos$ is adjacent over hypotenuse, $\sec$ of this angle is the hypotenuse over the adjacent side, which is $\sqrt{x^2 + 1}$.

Simplify the Express sec⁡(tan⁡−1x)\sec \left( \tan ^ { - 1 } x \right)sec(tan−1x)

Simplify the Express $\sec \left( \tan ^ { - 1 } x \right)$