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Popular >

f(x)=(tan^2(x))/(1+sec(x))

Solution

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

Solution

Period : 2 π

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

Range : f (x) < - 2 or f (x) \geq 0

Y Intercepts : (0, 0)

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

Extreme Points : None

+1

Interval Notation

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

Range : (- \infty, - 2) \cup [0, \infty)

Solution steps

Periodicity of

\frac{tan ^{2} ( x )}{1 + sec ( x )} : 2 π

Domain of

\frac{tan ^{2} ( x )}{1 + sec ( x )} : 2 πn \leq x < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < x < π + 2 πn or π + 2 πn < x < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < x < 2 π + 2 πn

Range of

\frac{tan ^{2} ( x )}{1 + sec ( x )} : f (x) < - 2 or f (x) \geq 0

Axis interception points of

\frac{tan ^{2} ( x )}{1 + sec ( x )} :

Y Intercepts

: (0, 0)

Asymptotes of

\frac{tan ^{2} ( x )}{1 + sec ( x )} :

Vertical

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

Extreme Points of

\frac{tan ^{2} ( x )}{1 + sec ( x )} :

None

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Frequently Asked Questions (FAQ)

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