You have 3434 of a pie leftover after your party. Each guest takes home 1616 of the leftover pie.

Roman55 [17]

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

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

In this problem we must prove that one side of the equality is equal to the expression of the other side, requiring the use of algebraic and trigonometric 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 trigonometric expression $\frac{\tan^{2} \alpha}{\tan \alpha - 1} + \frac{\cot^{2} \alpha}{\cot \alpha - 1}$ is equivalent to the trigonometric 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

5th grade math. correct answer will be marked brainliest

Yuliya22 [10]

Answer:

4ft, 7 inches

Step-by-step explanation:

4 ft (48 inches), 7 inches

4 0

3 years ago

Read 2 more answers

Need help with a math question PLEASE HELP

navik [9.2K]

Answer:

(-1, -3)

Step-by-step explanation:

We suppose your notation means you want to reflect given point P across the horizontal line y=1.

The x-coordinate will remain the same.

The new y-coordinate will be such that y=1 is the midpoint between the original and its reflection:

(5 + y)/2 = 1

5 + y = 2 . . . . multiply by 2

y = 2 -5 = -3 . . . subtract 5

The reflected point is (-1, -3).

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The same sort of math applies whenever you have a midpoint and want to find the other end point. Double the midpoint value and subtract the end point you have in order to find the other end point.

4 0

3 years ago

There are 4 colors of Starburst flavors: yellow, pink, red, and orange. If the probability of getting an orange is 2 5 2 5 , yel

trasher [3.6K]

Answer: 1/5

Step-by-step explanation:

From the question, we are informed that there are 4 colors of Starburst flavors: yellow, pink, red, and orange. We are further told that the probability of getting an orange is 2/5, yellow is 1/10 , and red is 3/10.

The probability of getting pink would be:

= 1 - [P(orange) + P(yellow) + P(red)]

= 1 - (2/5 + 1/10 + 3/10)

= 1 - (4/10 + 1/10 + 3/10)

= 1 - 8/10

= 2/10

= 1/5

5 0

2 years ago

Write the number 700000 + 400000 + 10000

DIA [1.3K]

That number would be 1,110,000.

5 0

2 years ago