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

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

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

domain

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

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

Interval Notation

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

Solution steps

Take the denominator(s) of

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

and compare to zero:

x = \frac{3 π}{2} + 2 πn

Periodicity of

\frac{cos ( x )}{1 + sin ( x )} : 2 π

Combine period:

2 πn \leq x < 2 π + 2 πn

and undefined points.

The domain is

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

f (x) = \frac{1}{5} - x

f (x) = x 3 - x

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

\frac{2 + 3 x}{x - 1}

f (x) = 4 sin (2 x + 5) - 7

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