Prove that (1-cos^2x)(1+cot^2x)=1

# Prove that (1-cos^2x)(1+cot^2x)=1

• MATH

Find the x intercepts of the graph: y = sec^4((pi x)/8) – 4

The x-intercepts of a graph, if there are any, are located where the y-coordinate is zero. So we can set the equation equal to zero and solve for x: sec^4((pi x)/8)-4=0 Factor as a quadratic:…

• MATH

Find the x intercepts of the graph: y = sin(pi x) + cos(pi x)

x-intercept is where y=0. Therefore we have the following equation: sin(pi x)+cos(pi x)=0 Now we square the whole equation. N.B. Sometimes when we square the whole equation we get some solutions…

• NATIVE SPEAKER

In the book Native Speaker, what is learned about male Koreanness at the end? In comparison,…

Henry Park is an incredibly complicated character; his facility with words and language is part of what has made him so successful in his job as a spy in the US, while in his private life the stoic…

• MATH

Find all solutions of the equation in the interval [0, 2pi). cos(x + pi) – cos(x) – 1 = 0

To find the solutions to this equation, we can use the trigonometric identity cos(x+pi) = -cos(x) Therefore the equation can be rewritten as -2cos(x) – 1 = 0 implies cos(x) = -1/2 `x =…

• MATH

Use the double angle formulas to verify the identity. tan^2x = (1-cos2x)/(1+cos2x)

The double angle formula we can use here to verify the equation given is the double angle formula for the cosine function: cos2x = cos^2(x) – sin^2(x) Substituting sin^2(x) = 1-cos^2(x) (from…

• MATH

Use the double angle formulas to verify the identity. sin4x = 8cos^3x*sinx – 4cosx*sinx

Start with the left hand side and try to get to the right hand side: sin(4x)=sin[2(2x)] Use sin2A=2sinAcosA: =2sin(2x)cos(2x) Again use sin2A=2sinAcosA:…

• SCIENCE

What are the main differences between physical and chemical change ? & some examples please.

There are marked differences between physical and chemical changes. Physical changes, typically, refer to changes in size, shape, texture, temperature, density, viscosity, etc. common examples…

• SHERMAN ALEXIE

What role is implied by the speaker’s self-presentation in Sherman Alexie’s Superman and Me?

Superman and Me is an autobiographical indictment of the moral and intellectual destruction inflicted on the Native American population by European interlopers. Sherman Alexie doesn’t come right…

• THE GREAT GATSBY

How are seasons used in constructing this novel The Great Gatsby?

As there are numerous films that include Summer in their titles, it is apparent that this season is strongly connected with stories of love, charged emotions, and passion. And, so, this season…

• WARRIORS DON’T CRY

What is the analysis of Warriors Don’t Cry?

There are lots of different ways to analyze Warriors Don’t Cry—it depends in part on what you feel you learned from it. Here are a couple ideas to get you started! Melba experiences terrible…

• THE BOY IN THE STRIPED PAJAMAS

In John Boyne’s The Boy in The Striped Pajamas, what is Pavel’s history?

During the events of the book, Pavel works in Bruno’s family home as a servant. Originally, he was a doctor. However, because he is Jewish, he has to be very careful. As a result, he is very…

• HAMLET

Choose six quotations from the first three acts of Hamlet that develop some line of logic in…

Shakespeare’s Hamlet is a drama in which appearance is contradictory to reality, actions contradictory to words, conduct contradictory to purpose. There is great deception and nothing…

• HISTORY

I need to make a satirical yearbook page for a well-known sinner (7 deadly sins). I have chosen…

Depicting Henry VIII in a satirical light is a worthy endeavor, given the late-monarch’s imperial excesses, particularly with respect to marriage. The man went through six wives, with wife…

• BIRCHES

Youth appears in Frost’s poem “Birches,” particularly in connection with innocence and its loss….

Robert Frost’s “Birches” is a rather nostalgic and rueful conversation between the speaker and the reader, whom he addresses as “you.” With the metaphor of swinging, the speaker takes the reader…

• REFERENCE

Concentration ranges of nitrogen? For a lake at Guangdong province, phosphorus concentration is…

The lakes exhibit nutrient limited growth depending on the TN:TP ratio, where TN and TP are total nitrogen and total phosphorus. Depending on various scientific literature, the range can be…

• CATHEDRAL

How does the protagonist change in “Cathedral”?

The protagonist is the narrator. He is shy and self-conscious. He needs liquor to loosen up with people. He is afraid of strangers, and he feels jealous of the blind man named Robert who is coming…

• DANTE’S INFERNO

In Dante’s Inferno, what was Dante saying about the people of the time?

The original title for Dante Alighieri’s work was simply “Commedia,” or Comedy (“Divina,” or Divine, was added later in the 16th C.). In contrast to the other major genres of the period (myth,…

• THE INTUITIONIST

How can I connect the character of Lila Mae from “The Intutionist” to other African American…

Let’s think about the characteristics of Lila Mae and how they might relate to other characters in African American literature. Lila Mae is marginalized by her race, sex, and her ability to…

• FAIL-SAFE

What are the similarities and differences in the book and the film Fail Safe?

There are actually two different films based on the book Fail Safe (one from the mid 1960s and one from the year 2000). I am guessing that you want a comparison of the book and the more recent…

Explain what causes economies of scale. Can economies of scale and diminishing marginal returns…

Economies of scale exist when a firm expands its production and sees its long-run average costs decrease. In a situation like this, being bigger helps a firm. If a firm grows larger, its costs…

• FAIL-SAFE

Comparison/analysis of the book Fail-Safe and the film.

Please keep in mind that there were two films made from the Fail Safe novel. One was made in 1964 and one was made in 2000. I am assuming you are speaking about the more recent film. If that is…

• JULIUS CAESAR

In the play Julius Caesar, what are two ways Antony betrayed Caesar?

Mark Antony was generally a close friend and confidant of Julius Caesar. Antony joined Caesar’s staff and was a member of his army. Caesar appointed him to military leadership, a role he…

• THE NAMESAKE

How does Ashima and Ashoke’s immigration affect Gogol?

Ashima and Ashoke’s immigration has a profound impact on their son Gogol. He grows up surrounded by friends and peers who understand and move comfortably in American culture in a way his family…

• ROMEO AND JULIET

What is Shakespeare’s purpose in the delaying tactics of the Nurse in Romeo and Juliet?

The comic character of the Nurse displays a fickleness at certain points in Shakespeare’s play that defies explanation, especially in Act IV, Scene 5 when she urges Juliet to marry Paris although…

• SORROW-ACRE

What symbolism does the weather have in “Sorrow-Acre” in relevance to Adam and Anne-Marie?

Izak Dinesen is the pen-name for Karen Bliksen (nee Dinesen) who is famous for her biography Out of Africa which was adapted by Kurt Luedtke and made into a movie that won Academy Awards (Oscars)…

• HISTORY

Why could the period of Reconstruction 1865-1877 be considered a failure in the Unites States’…

The period of Reconstruction can be considered a failure in the United States’ attempts to improve social and political equality because African Americans came out of the Reconstruction Era not…

• REFERENCE

What is a double autobiography?

A double autobiography or dual autobiography is an autobiography jointly about two people. These would naturally be people who live entwined lives (have an ongoing close relationship), such as…

• HISTORY

True or False Progressive intellectuals, social scientists, labor reformers, and suffrage…

The answer to the question – were progressive intellectuals, labor reformers, and suffragettes supportive of and/or active in the civil rights movement – is yes, they were. Most progressives,…

• IF

What are some alliteration, assonance, and symbols in the poem IF by Rudyard Kipling?

Alliteration: And—which is more—you’ll be a Man, my son! Twisted by knaves to make a trap for fools Assonance: And yet don’t look too good, nor talk too wise Symbols: “Walk with Kings”:…

• OF MICE AND MEN

What ideas does Steinbeck develop in Of Mice and Men regarding the affect of adversity on the…

The Great Depression brought adversity not just to individuals, but to an entire socio-economic class. Because so many men were dispossessed, the impact upon them was profound. Loss The “bindle…

• ESSAY LAB

My family is a small family with three people. My mother is a great woman . She is currently…

For the most part, your grammatical constructions are correct. In the 4th sentence, however, you will want to change the verb took to has taken (present Perfect tense, meaning the action started in…

• MATH

What square number divides exactly into 50? Is it 25? Which of the surds below can be simplified…

(I) To solve, apply the divisibility rules of numbers. Since 50 ends with 0, it means that it is divisible by the prime numbers 2 and 5. 50 -:2 = 2550-:5=10 Between these two results, 25 is…

• CHRONICLE OF A DEATH FORETOLD

Chronicle Of A Death Foretold- What is the purpose and scope of literature in the culture of…

In referring to the culture of origin, I am unsure whether you are referencing the context in which this novel was published (Colombia 1981) or the fictional setting of the novel (a Colombian…

• HISTORY

Eric Foner writes, “prejudice by itself did not create North American slavery.” Examine what did…

Foner makes the argument that slavery was so complex that it could not be reduced to one distinct force of causation. Prejudice was one part of this construction. However, Foner feels that there…

• HISTORY

In what ways did the New England Colonies’ economy and society differ from the Chesapeake…

Geography and climate proved to have a significant impact on developing the economies of both the New England and Chesapeake Colonies. The New England Colonies included those of Connecticut, the…

• MATH

sqrt(a^(16)b) How to solve it? When is sqrt(y)not defined in the real number system? a)…

(I) sqrt(a^16b) To simplify this, take the square root of each factor. =sqrt(a^16) * sqrtb Since the index of the radical is 2, a factor that has an even number exponent can be simplified. It…

• HISTORY

For the English, land was the basis of liberty. Explain the reasoning behind that concept, and…

For the English, land was the basis of freedom and liberty because land allowed people to have control of their own labor. A person who did not own land was not in control of their labor. Since…

• HISTORY

Describe why the “discovery” of America was one of the “most important events recorded in the…

Although Adam Smith does say that the discovery of the Americas (along with the discovery of a trade route around Africa to Asia) was one of the “greatest and most important events recorded in…

• A VERY OLD MAN WITH ENORMOUS WINGS

How does Gabriel Garcia Marquez use animals, elements of earth and sky, and irony in his language…

There is a Biblical verse relevant to this story which states, Be not forgetful to entertain strangers: for thereby some have entertained angels. Marquez’s story has, indeed, timeless themes such…

• CHRONICLE OF A DEATH FORETOLD

In Gabriel Garcia Marquez’s Chronicle of a Death Foretold, how could one describe the economy of…

The state of the economy in Garbriel Garcia Marquez’s Colombia of the 1930s and 1950s, the periods when much of Chronicle of the Death Foretold takes place, is not a particular focus of the…

• THE GREAT GATSBY

What symbol does Fitzgerald use as the outward manifestation of Gatsby’s wealth? What theme does…

When Gatsby takes Nick and Daisy to his mansion, he shows Daisy all his worldly treasures. In his bedroom, he shows her all of his shirts: “I’ve got a man in England who buys me clothes. He…

• MATH

35-(10 3/5 + 12 1/2)

Before we can combine the fractions, we need to make the denominators equal. To do that, we need to identify the LCD (least common denominator).Identifying the LCD is the same as identifying the…

• HISTORY

Was the Aroostook War of Maine in 1842 a joke or was something else more serious going on?

What has been called the Aroostook War of Maine was a hostile dispute between England and Maine, a confrontation (sometimes referred to as the Pork and Beans War in historical reviews) that…

• A TALE OF TWO CITIES

Why does Dr. Manette make shoes in A Tale of Two Cites?

Dr. Manette makes shoes because he made shoes while he was in prison, and when he gets stressed he has a mental relapse and makes shoes. Dr. Manette was locked in the Bastille prison for 18 years…

• THE STONE BOY

What are the different types of conflicts in the short story “The Stone Boy” by Gina Berriault?

I think that one conflict that exists in the story is the conflict between Arnold and his parents upon receiving the news that Eugie is dead. The family is in conflict because they are unaware of…

• A MAGNIFICENT CATASTROPHE

What are the positive and negative aspects of Edward Larson’s nonfiction book A Magnificent…

When critiquing Edward Larson’s history of the politics of the early years of the nation’s founding, describing the positives and the negatives of Larson’s study is a little depressing. The…

• THE LAKE ISLE OF INNISFREE

How do you pronounce “Yeats” as in William Butler Yeats? Add a note on the poem “The Lake Isle of…

The poet William Butler Yeats’s last name rhymes with hates. You can listen to Yeats pronounced on the youtube link cited below. William Butler Yeats is generally regarded as one of the finest…

• LITERATURE

How does one make a three-question quiz about the literary word parable?

You could use a passage in your quiz. Summarize three stories, and ask the students which one is the parable. Other questions: How is a parable different from a fable? (Fables use animals or…

Discuss the impact of changes in the size of the 18-24 age group on marketing strategy planning…

The impact of changes in the size of the 18-24 age group on marketing strategy planning in the United States means ascertaining the changes that may be required in the marketing budget, primarily….