What is the domain of tan(x+2) ?

The domain of tan(x+2) is pin<= x<(3pi-4)/2+pin\lor (3pi)/2-2+pin<x<pi+pin

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domain of tan(x+2)

domain

πn \leq x < \frac{3 π - 4}{2} + πn or \frac{3 π}{2} - 2 + πn < x < π + πn

Interval Notation

[πn, \frac{3 π - 4}{2} + πn) \cup (\frac{3 π}{2} - 2 + πn, π + πn)

Solution steps

Take the denominator(s) of

tan (x + 2)

and compare to zero:

x = \frac{3 π - 4}{2} + πn, x = \frac{3 π}{2} - 2 + πn

Periodicity of

tan (x + 2) : π

Combine period:

πn \leq x < π + πn

and undefined points.

The domain is

πn \leq x < \frac{3 π - 4}{2} + πn or \frac{3 π}{2} - 2 + πn < x < π + πn

What is the domain of tan(x+2) ?
The domain of tan(x+2) is pin<= x<(3pi-4)/2+pin\lor (3pi)/2-2+pin<x<pi+pin