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Popular >

f(x)=tan^2(x)+cot^2(x)

Solution

f (x) = tan^{2} (x) + cot^{2} (x)

Solution

Period : π

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

Range : f (x) \geq 2

Intercepts : None

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

Extreme Points : Minimum (\frac{π}{4} + πn, 2), Minimum (\frac{3 π}{4} + πn, 2)

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Solution steps

Periodicity of

tan^{2} (x) + cot^{2} (x) : π

Domain of

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

Range of

tan^{2} (x) + cot^{2} (x) : f (x) \geq 2

Axis interception points of

tan^{2} (x) + cot^{2} (x) :

None

Asymptotes of

tan^{2} (x) + cot^{2} (x) :

Vertical

: x = \frac{π}{2} + πn, x = πn

Extreme Points of

tan^{2} (x) + cot^{2} (x) :

Minimum

(\frac{π}{4} + πn, 2),

Minimum

(\frac{3 π}{4} + πn, 2)

Popular Examples

f (x) = x^{2} + 8 x + 10

f (t) = \frac{1}{t}

y = ∣ x - 4 ∣

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

y = 6 x - 11

Frequently Asked Questions (FAQ)

What is the f(x)=tan^2(x)+cot^2(x) ?
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