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Popular >

f(x)=(1+tan(x))/(1+cot(x))

Solution

f (x) = \frac{1 + tan ( x )}{1 + cot ( x )}

Solution

Period : π

Domain : πn < x < \frac{π}{2} + πn or \frac{π}{2} + πn < x < \frac{3 π}{4} + πn or \frac{3 π}{4} + πn < x < π + πn

Range : f (x) < - 1 or - 1 < f (x) < 0 or f (x) > 0

Intercepts : None

Asymptotes : Vertical x = \frac{π}{2} + πn

Extreme Points : None

+1

Interval Notation

Domain : (πn, \frac{π}{2} + πn) \cup (\frac{π}{2} + πn, \frac{3 π}{4} + πn) \cup (\frac{3 π}{4} + πn, π + πn)

Range : (- \infty, - 1) \cup (- 1, 0) \cup (0, \infty)

Solution steps

Periodicity of

\frac{1 + tan ( x )}{1 + cot ( x )} : π

Domain of

\frac{1 + tan ( x )}{1 + cot ( x )} : πn < x < \frac{π}{2} + πn or \frac{π}{2} + πn < x < \frac{3 π}{4} + πn or \frac{3 π}{4} + πn < x < π + πn

Range of

\frac{1 + tan ( x )}{1 + cot ( x )} : f (x) < - 1 or - 1 < f (x) < 0 or f (x) > 0

Axis interception points of

\frac{1 + tan ( x )}{1 + cot ( x )} :

None

Asymptotes of

\frac{1 + tan ( x )}{1 + cot ( x )} :

Vertical

: x = \frac{π}{2} + πn

Extreme Points of

\frac{1 + tan ( x )}{1 + cot ( x )} :

None

Popular Examples

f(x)=arctan(1/x)

f (x) = arctan (\frac{1}{x})

y = 2 - x

f (x) = x^{2} + 6 x + 5

f(x)= x/(x^2+4)

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

y = 8 x

Frequently Asked Questions (FAQ)

What is the f(x)=(1+tan(x))/(1+cot(x)) ?
The f(x)=(1+tan(x))/(1+cot(x)) is