What is the domain of sec(x)csc(x) ?

The domain of sec(x)csc(x) is pin<x< pi/2+pin\lor pi/2+pin<x<pi+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

domain of sec(x)csc(x)

domain

sec (x) csc (x)

πn < x < \frac{π}{2} + πn or \frac{π}{2} + πn < x < π + πn

Interval Notation

(πn, \frac{π}{2} + πn) \cup (\frac{π}{2} + πn, π + πn)

Solution steps

Take the denominator(s) of

sec (x) csc (x)

and compare to zero:

x = \frac{π}{2} + πn, x = πn

Periodicity of

sec (x) csc (x) : π

Combine period:

πn \leq x < π + πn

and undefined points.

The domain is

πn < x < \frac{π}{2} + πn or \frac{π}{2} + πn < x < π + πn

What is the domain of sec(x)csc(x) ?
The domain of sec(x)csc(x) is pin<x< pi/2+pin\lor pi/2+pin<x<pi+pin