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

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

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

Interval Notation

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

y = \frac{1 - e ^{x^{2}}}{1 - e ^{1 - x^{2}}}

f (x) = (3 x - 3)

f (x) = - 8 x - 3

\frac{14 x ^{2}}{x ^{4} + 49}

y = \frac{1}{2} cos (x) - 2

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