What is the domain of f(x)=1-sec(2x)*csc(2x) ?

The domain of f(x)=1-sec(2x)*csc(2x) is pi/2 n<x< pi/4+pi/2 n\lor pi/4+pi/2 n<x< pi/2+pi/2 n

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domain of f(x)=1-sec(2x)*csc(2x)

domain

\frac{π}{2} n < x < \frac{π}{4} + \frac{π}{2} n or \frac{π}{4} + \frac{π}{2} n < x < \frac{π}{2} + \frac{π}{2} n

Interval Notation

(\frac{π}{2} n, \frac{π}{4} + \frac{π}{2} n) \cup (\frac{π}{4} + \frac{π}{2} n, \frac{π}{2} + \frac{π}{2} n)

Solution steps

Take the denominator(s) of

1 - sec (2 x) \cdot csc (2 x)

and compare to zero:

x = \frac{π}{4} + \frac{π}{2} n, x = \frac{π}{2} n

Periodicity of

1 - sec (2 x) \cdot csc (2 x) : \frac{π}{2}

Combine period:

\frac{π}{2} n \leq x < \frac{π}{2} + \frac{π}{2} n

and undefined points.

The domain is

\frac{π}{2} n < x < \frac{π}{4} + \frac{π}{2} n or \frac{π}{4} + \frac{π}{2} n < x < \frac{π}{2} + \frac{π}{2} n

What is the domain of f(x)=1-sec(2x)*csc(2x) ?
The domain of f(x)=1-sec(2x)*csc(2x) is pi/2 n<x< pi/4+pi/2 n\lor pi/4+pi/2 n<x< pi/2+pi/2 n