Which types of parent function have the end behavior f(x) - infinity as x

Roman55 [17]

The <em>trigonometric</em> expression $\frac{\tan^{2} \alpha}{\tan \alpha - 1} + \frac{\cot^{2} \alpha}{\cot \alpha - 1}$ is equivalent to the <em>trigonometric</em> expression $\sec \alpha \cdot \csc \alpha + 1$ .

<h3>How to prove a trigonometric equivalence</h3>

In this problem we must prove that <em>one</em> side of the equality is equal to the expression of the <em>other</em> side, requiring the use of <em>algebraic</em> and <em>trigonometric</em> properties. Now we proceed to present the corresponding procedure:

$\frac{\tan^{2} \alpha}{\tan \alpha - 1} + \frac{\cot^{2} \alpha}{\cot \alpha - 1}$

$\frac{\tan^{2}\alpha}{\tan \alpha - 1} + \frac{\frac{1}{\tan^{2}\alpha} }{\frac{1}{\tan \alpha} - 1 }$

$\frac{\tan^{2}\alpha}{\tan \alpha - 1} - \frac{\frac{1 }{\tan \alpha} }{\tan \alpha - 1}$

$\frac{\frac{\tan^{3}\alpha - 1}{\tan \alpha} }{\tan \alpha - 1}$

$\frac{\tan^{3}\alpha - 1}{\tan \alpha \cdot (\tan \alpha - 1)}$

$\frac{(\tan \alpha - 1)\cdot (\tan^{2} \alpha + \tan \alpha + 1)}{\tan \alpha\cdot (\tan \alpha - 1)}$

$\frac{\tan^{2}\alpha + \tan \alpha + 1}{\tan \alpha}$

$\tan \alpha + 1 + \cot \alpha$

$\frac{\sin \alpha}{\cos \alpha} + \frac{\cos \alpha}{\sin \alpha} + 1$

$\frac{\sin^{2}\alpha + \cos^{2}\alpha}{\cos \alpha \cdot \sin \alpha} + 1$

$\frac{1}{\cos \alpha \cdot \sin \alpha} + 1$

$\sec \alpha \cdot \csc \alpha + 1$

The <em>trigonometric</em> expression $\frac{\tan^{2} \alpha}{\tan \alpha - 1} + \frac{\cot^{2} \alpha}{\cot \alpha - 1}$ is equivalent to the <em>trigonometric</em> expression $\sec \alpha \cdot \csc \alpha + 1$ .

To learn more on trigonometric expressions: brainly.com/question/10083069

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6 0

2 years ago

What is a summary number model :) by the way here is the question joe ordered 72 plants for his patio garden.

Nitella [24]

18 pots because 4 times 18 equals 72

8 0

4 years ago

Read 2 more answers

Need help real fast.

Nutka1998 [239]

Answer:

k=-2

Step-by-step explanation:

-1*-2=2

-1*-2=20*-2=0

-1*-2=20*-2=02*-2=-4

-1*-2=20*-2=02*-2=-45*-2=10

4 0

3 years ago

Find P(B|C). P(B|C) = StartFraction 9 Over 34 EndFraction = 0. 26 P(B|C) = StartFraction 9 Over 24 EndFraction = 0. 38 P(B|C) =

Kruka [31]

The question is an illustration of probability, and the value of P(B|C) is P(B|C) = 9/24 =0.38

<h3>How to determine the probability P(B|C)?</h3>

The table is given as:

C D Total

A 15 21 36

B 9 25 34

Total 24 46 70

The probability (BIC) is calculated using:

P(B|C) = n(B and C)/n(C)

From the table, we have:

n(B and C) = 9

n(C) = 24

So, the equation becomes

P(B|C) = 9/24

Evaluate

P(B|C) = 0.38

Hence, the value of P(B|C) is P(B|C) = 9/24 =0.38

Which types of parent function have the end behavior f(x) - infinity as x - infinity