MHB What are the points of discontinuity for the function $f(x,y)$?

[Dustinsfl]

Points of discontinuity
$f(x,y) = \begin{cases}\frac{\sin x - \sin y}{\tan x - \tan y}, & \text{if } \tan x\neq\tan y\\
\cos^3 x, & \text{if } \tan x = \tan y\end{cases}$
Not sure what to do with this one.

 

[chisigma]

Points of discontinuity
$f(x,y) = \begin{cases}\frac{\sin x - \sin y}{\tan x - \tan y}, & \text{if } \tan x\neq\tan y\\
\cos^3 x, & \text{if } \tan x = \tan y\end{cases}$
Not sure what to do with this one.

The denominator vanishes if $\displaystyle y = x + n\ \pi$, n being an integer. The numerator vanishes if $\displaystyle y= x + 2\ k\ \pi$, k being and integer, and in these points f(*,*) is continous, not if $\displaystyle y = x + (2\ k +1)\ \pi$, k being an integer, and in these points f(*,*) is discontinous...

Kind regards

$\chi$ $\sigma$