Question #299c9

Question

1152 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-05-07T22:49:24

The expression is undefined.

(A problem with similar structure linked here)

Simplify the trig terms by imagining the unit circle, or breaking the terms down into $sin$ and $cos$ :

$ln(sec(pi/2)+tan(pi/2))-ln(sec0+tan0)$

$=ln(1/cos(pi/2) + sin(pi/2)/cos(pi/2))-ln(1+0)$

We know $ln1=0$ because of the properties of logarithms
$=ln(frac{1+sin(pi/2)}{cos(pi/2)})-0$

$=ln(frac{2}{cos(pi/2)})$

Since $cos (pi/2) = 0$ is in the denominator of the fraction inside the natural log, the expression is undefined.

Separately however, if this problem started out as $int_0^(pi/2) (secx)dx$ , then click here to look at the solution to the improper integral.