What is the domain of y= 1/(sec^2(x))+1/(csc^2(x)) ?

The domain of y= 1/(sec^2(x))+1/(csc^2(x)) is pin<x< pi/2+pin\lor pi/2+pin<x<pi+pin

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domain of y= 1/(sec^2(x))+1/(csc^2(x))

domain

y = \frac{1}{sec ^{2} ( x )} + \frac{1}{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

\frac{1}{sec ^{2} ( x )} + \frac{1}{csc ^{2} ( x )}

and compare to zero:

x = \frac{π}{2} + πn, x = πn

Periodicity of

\frac{1}{sec ^{2} ( x )} + \frac{1}{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 y= 1/(sec^2(x))+1/(csc^2(x)) ?
The domain of y= 1/(sec^2(x))+1/(csc^2(x)) is pin<x< pi/2+pin\lor pi/2+pin<x<pi+pin