What is the domain of (sin(2x))/(1+sin(2x)) ?

The domain of (sin(2x))/(1+sin(2x)) is pin<= x<(3pi)/4+pin\lor (3pi)/4+pin<x<pi+pin

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domain of (sin(2x))/(1+sin(2x))

domain

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

Interval Notation

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

Solution steps

Take the denominator(s) of

\frac{sin ( 2 x )}{1 + sin ( 2 x )}

and compare to zero:

x = \frac{3 π}{4} + πn

Periodicity of

\frac{sin ( 2 x )}{1 + sin ( 2 x )} : π

Combine period:

πn \leq x < π + πn

and undefined points.

The domain is

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

What is the domain of (sin(2x))/(1+sin(2x)) ?
The domain of (sin(2x))/(1+sin(2x)) is pin<= x<(3pi)/4+pin\lor (3pi)/4+pin<x<pi+pin