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Popular >

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

Solution

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

Solution

Period : 2 π

Domain : 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

Range : f (x) \leq - \frac{2}{2} or f (x) \geq \frac{1}{2}

Y Intercepts : (0, 1)

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

Extreme Points : Minimum (\frac{π}{4} + 2 πn, \frac{1}{2}), Maximum (\frac{5 π}{4} + 2 πn, - \frac{2}{2})

+1

Interval Notation

Domain : [2 πn, \frac{π}{2} + 2 πn) \cup (\frac{π}{2} + 2 πn, \frac{3 π}{4} + 2 πn) \cup (\frac{3 π}{4} + 2 πn, \frac{3 π}{2} + 2 πn) \cup (\frac{3 π}{2} + 2 πn, \frac{7 π}{4} + 2 πn) \cup (\frac{7 π}{4} + 2 πn, 2 π + 2 πn)

Range : (- \infty, - \frac{2}{2}] \cup [\frac{1}{2}, \infty)

Solution steps

Periodicity of

\frac{sec ( x )}{1 + tan ( x )} : 2 π

Domain of

\frac{sec ( 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

Range of

\frac{sec ( x )}{1 + tan ( x )} : f (x) \leq - \frac{2}{2} or f (x) \geq \frac{1}{2}

Axis interception points of

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

Y Intercepts

: (0, 1)

Asymptotes of

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

Vertical

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

Extreme Points of

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

Minimum

(\frac{π}{4} + 2 πn, \frac{1}{2}),

Maximum

(\frac{5 π}{4} + 2 πn, - \frac{2}{2})

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Frequently Asked Questions (FAQ)

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