What is the domain of csc(2x) ?

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

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domain of csc(2x)

domain

csc (2 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

csc (2 x)

and compare to zero:

x = πn, x = \frac{π}{2} + πn

Periodicity of

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