What is $\tan{\frac{\pi}{2}}$ ?

Level 2

What is $\large \frac{1 - \cot{\frac{\pi}{2}}}{1 + \cot{\frac{\pi}{2}}} ?$

\sqrt{3}

\frac{1}{2}

\frac{1}{\sqrt{2}}

undefined

\frac{1}{\sqrt{3}}

\pi

\frac{\sqrt{3}}{2}

1

2 solutions

Chew-Seong Cheong
Dec 27, 2018

$\dfrac {1-\cot \frac \pi 2}{1+\cot \frac \pi 2} = \dfrac {1-0}{1+0} = \boxed 1$

Hi, may I know how would you solve the following?

$\frac{\tan{\frac{\pi}{2}} -1}{\tan{\frac{\pi}{2}}+1}$

Note that $\tan{\frac{\pi}{2}}$ is undefined, not $\infty$ .

You can only say that for $x < \frac{\pi}{2}$ ,

as $x \rightarrow \frac{\pi}{2}$ , $\tan{x} \rightarrow \infty$ .

Note that for all $x$ , $x \ne \frac{\pi}{2}$ .

Lucas Tan - 2 years, 5 months ago

No, as $x \to \infty$ , $\tan x$ is undefined because it can take all values from $(-\infty, \infty)$ .

Chew-Seong Cheong - 2 years, 5 months ago

Sorry, have edited it to $\frac{\pi}{2}$ , it was a typo.

Lucas Tan - 2 years, 5 months ago

Lucas Tan
Dec 26, 2018

$\frac{1 - \cot{\frac{\pi}{2}}}{1 + \cot{\frac{\pi}{2}}}$

$= \frac{\tan{\frac{\pi}{2}}-1}{\tan{\frac{\pi}{2}}+1}$

$= \frac{\tan{\frac{\pi}{2}}+\tan{(- \frac{\pi}{4}})}{1 - \tan{\frac{\pi}{2}} \tan{(- \frac{\pi}{4}})}$

$= \tan{(\frac{\pi}{2} - \frac{\pi}{4})}$

$= \tan{\frac{\pi}{4}}$

$= 1$