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

The domain of (cos(x))/(1+tan(x)) is

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

domain

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

2 πn \leq x < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < x < \frac{3 π}{4} + 2 πn or \frac{3 π}{4} + 2 πn < x < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < x < \frac{7 π}{4} + 2 πn or \frac{7 π}{4} + 2 πn < x < 2 π + 2 πn

Interval Notation

Solution steps

Take the denominator(s) of

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

and compare to zero:

x = \frac{3 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn, x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Periodicity of

\frac{cos ( x )}{1 + tan ( x )} : 2 π

Combine period:

2 πn \leq x < 2 π + 2 πn

and undefined points.

The domain is

2 πn \leq x < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < x < \frac{3 π}{4} + 2 πn or \frac{3 π}{4} + 2 πn < x < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < x < \frac{7 π}{4} + 2 πn or \frac{7 π}{4} + 2 πn < x < 2 π + 2 πn

f (x) = \frac{x - 4}{x ^{2} + 3 x - 40}

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

f (x) = ln (5 t + 10)

f (x) = 3 \frac{y}{( ( y - 6 ) )}

f (x) = \frac{3 x + 4 x}{x ^{2} + 7 x + 12}

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