Prove that arctan (2+sqrt3)+arctan (2-sqrt3)=pi/2!

# Prove that arctan (2+sqrt3)+arctan (2-sqrt3)=pi/2!

• MATH

Solve x^[(lgx + 1)/lgx]=100

x^ (lgx + 1)/lgx = 100 First let take log for both sides: lg x^(1gx+1)/lgx = lg 100 We know that log a^b = b log a ==> [(lgx +1)/lgx]*lg x = lg 10^2 Reduce similar: ==> lg x + 1 = 2log 10…

• MATH

Prove that arctan (2+sqrt3)+arctan (2-sqrt3)=pi/2!

Let us assume that: arctan (2+ sqrt3) = x arcttan (2-sqrt3) = y ==> tanx = 2+ sqrt3 ==> tany = 2-sqrt3 Now we know that: tan (x+y) = (tanx + tany)/[1- tanx*tany] ==> tan (arctan (2+…

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What are five causes that will make you not trust the goverment, and what are five causes that…

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• MATH

Solve the equation (3+2sqrt2)^x + (3-2sqrt2)^x=34

3+ 2sqrt2)^x + (3-2sqrt2)^x = 34 We know thta: 3+2sqrt2 = 1/(3-2sqrt2) Now substitute: ==> (1/(3-2sqrt2)^x + (3-2sqrt2)^x = 34 ==> (3-2sqrt2)^-x + (3-2sqrt2)^x = 34 Let y= (3-2sqrt3)^x ==>…

• MATH

Determine x if 6^x – 5^x = 4^x – 3^x .

6^x – 5^x = 4^x -3^x Let us substitute with c=0: ==> 6^0 – 5^0 = 4^0 – 3^0 ==> 1- 1 = 1-1 = 0 Then: x1= 0 is one of the solutions: Now subsotute with x=1: ==> 6^1 – 5^1 = 4^1 – 3^1…

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What is and what are the “Poco Issues”?

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• MATH

Given that x^2 – 2*f(x) = f(1/x) determine f(2)

x^2 – 2*f(x) = f(1/x) Let us substitue with x= 2: 2^2 – 2f(2) = f(1/2) 4- 2f(2) = f(1/2) ==> f(1/2) = 4-2f(2) ……..(1) Now subsitute with x= 1/2 ==> (1/4) – 2f(1/2) = f(2) ==> f(1/2) =…

• AS YOU LIKE IT

Critical analysis of As You Like It?

When a teacher/professor asks you for a critical analysis of a text, he/she does not want you to actually criticize the play in terms of looking for errors or mistakes. What a critical analysis of…

• MATH

Solve the equation 2iz/(1 – i) + 2i = 2z(1 – i) – 3 + i

2iz / (1-i) + 2i = 2z (1-i) -3 + i Let z = a+ bi ==> 2i(a+bi)/ (1-i) + 2i = 2(a+bi)(1-i) -3 + i Multiply by (1-i): ==> 2i(a+bi) + 2i(1-i) = 2(a+bi)(1-i)(1-i) -3(1-i)+ i(1-i) ==> 2ai – 2b…

• SCIENCE

Does the personal health ever intersect with public health?

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• MATH

If the points A(2,3+a), B(a-1,2a), C(3,5) are on the line calculate a.

A (2, 3+a) , B(a-1, 2a) C (3, 5) The point are on the same line, Then slope AB = slope BC = slope (AC slope AC = ((5-(3+a)/(3-2)= (2-a) slope BC= (5-2a)/(3-(a-1) = (5-2a)/ (4-a) We know that…

• WHERE ARE YOU GOING, WHERE HAVE YOU BEEN?

Why do you have to count backwards from the last book of the old testament to find Judges when…

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• MATH

Calculate |[(3-4i)/(5+12i)]^2|.

The line numbers vary depending on what translation of Beowulf you are studying, so I can’t refer you to specific lines. Beowulf says he is as brave and fearless as Grendel, so he will use no…

• POETRY

How do I do a reader response to “Sailing to Byzantium” by William Butler Yeats?Can you refer to…

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• HENRY

What is the climax of the story “The Last Leaf ” by O.Henry?

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• POETRY

Analyze “The Whipping” by Robert Hayden utilizing either a biographical or historical…

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• MATH

Solve the equation (3-2*sqrt2)^x + 2(sqrt2-1 )^x = 1

This is an exponential equation and we’ll use the substitution technique to solve it. We notice that we’ll raise to square (sqrt2-1 )^2, we’ll get: (sqrt2-1 )^2 = 2 – 2sqrt2 + 1 = 3 – sqrt2 So,…

• POETRY

How do I do formalist criticism of “Spring and All” by William Carlos Williams, and how can it be…

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• 1984

What actions in 1984, by George Orwell, signals the end of Winston’s humanity?

In my opinion, the event that signals the end of Winston’s humanity is when he betrays Julia. I think that this shows him giving up his human emotions so as to just be able to get along in his…

• MATH

Solve for x sqrt(2x+5) = sqrt(x+2) + sqrt(2x-3).

sqrt(2x+5) = sqrt(x+2) + sqrt(2x-3) Let us square both sides: ==> (2x+5) = (x+2) + 2sqrt(x+2)(2x-3) + (2x-3) ==> (2x+5) = x+2 + 2x -3 + 2sqrt(2x^2 +x -6) ==> (2x+5) = 3x -1 + 2sqrt(2x^2 +…

• LAW AND POLITICS

Why do you think the 4th Amendment is important?

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• THE BLUEST EYE

Why does Frieda seem to handle sexual abuse better than Pecola??

The answer most probably lies with the difference in the Breedlove and Macteer families. While the Macteer family is poor, and the girls often feel that their parents treat them harshly, there is…

• MATH

Solve log 1/2 (2x^2 + x + 1) >= -1

log 1/2 (2x^2 + x + 1 ) >=-1 ==> 2x^2 + x +1 >= (1/2)^-1 ==> 2x^2 + x + 1 >= 2 Now subtract 2 from both sides: ==> 2x^2 + x -1 >= 0 Now let us factorise: ==> (2x -1)(x+1)…

• MATH

Determine the roots of f”(x) if f(x)= x/(x^2+1) .

f(x) = x/(x^2+1) First let us assume that: f(x) = u/v such that: u= x ==> u’ = 1 v= x^2 + 1 ==> v’= 2x f'(x) = (u’v-uv’)/v^2 = (x^2+1) – 2x^2]/(x^2+1)^2 =…

• MATH

Solve for x and y 4x+ 5y = 10, 6x – 5y = 5.

4x + 5y = 10…….(1) 6x -5y = 5………..(2) Using the elimination method, add (1) and (2): ==> 10x = 15 ==> x = 15/10 = 3/2 ==> x= 3/2 Now to calculate y, let us substitute with (2):…

• MATH

Calculate f'(x) = 0 if f(x) = x/(1+x^2)

f'(x) = 0 f(x) = x/(1+x^2) assume that: f(x) = u/v such that: u = x ==> u’=1 v= 1+x^2 ==> v’ = 2x f'(x) = (u’v- uv’)/v^2 = 1(1+x^2) – x(2x)]/(1+x^2)^2 = (1+ x^2 -…

• MATH

Determine the function f=ln(x+1) – a*x if the function is increasing on the interval (-1;infinite).

f(x) = ln (x+1) – ax The function is increasing on the interval (-1, infinite) Then, the first derivative ‘f'(x)” is positive on the interval (-1, inf.) Let us calculate first derivative: f'(x) =…

• ANIMAL FARM

How does Orwell indicate that Frederick and Pilkington are “thoroughly frightened” by the events…

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• SCIENCE

Which is the recomended daily zinc intake?

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• A PORTRAIT OF THE ARTIST AS A YOUNG MAN

Who is the little boy that Moocow meets in James Joyce’s “A Portrait of the Artist as a Young…

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• LITERATURE

What are the themes of Dairy Queen by Catherine Gilbert Murdock?Is there another theme to Dairy…

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• SCIENCE

What are the cranial nerves?

Cranial nerves are nerves which rise directly from the brain unlike nerves which rise from the spinal chord. They are twelve in number. They are: 1. Olfactory. The sense of smell is carried by the…

• SOCIAL SCIENCES

In democracy who governs and what is the citizen participation?no

In a democracy, the people are the ones who ultimately have the power, but I suppose you would say that it is the government (elected by the people) that governs. In a democracy, the people elect…

• SCIENCE

Calculate the density of any metal and explain how you did it.

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• ARMS AND THE MAN

What is the main theme of Shaw’s Arms and the Man?

Shaw’s title of his play, Arms and the Man is taken from the opening line of Virgil’s epic The Aeneid – “Of arms and the man I sing.” The play was first produced on April 21st 1894 and was a huge…

• SCIENCE

What is the basic principle of holography?I mean the main terms and a short reasonable explanation.

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• ANIMAL FARM

Are the characters in Animal Farm stereotypes?If so, explain the usefulness of employing…

When creating an allegorical story, the author–to a certain degree–must employ stereotypes to make the characters fit into symbolic molds. If Animal Farm is to be a satire of the Russian…

• ANIMAL FARM

Discuss each character in terms of its animal and human nature in Animal Farm.

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• SCIENCE

Using scientific terminologyI am looking for new ideas on improving student’s science vocabulary….

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• ELIZABETHAN DRAMA

What are the secular influnces on the Early English Drama?

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• SCIENCE

Give three examples from our daily life to show how important it is for gases to diffuse quickly.

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• LORD OF THE FLIES

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• SCIENCE

Molecular mass of chlorine, nitrogen, sulphur dioxide & carbon dioxide are 71, 28, 64, 44…

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• ROMEO AND JULIET

How are hate and revenge displayed in Romeo and Juliet?What actions and quotes are said to prove…

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What do you think about gender discrimination at the workplace? Examples please.What do you think…

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• CANDIDE

Drawing from the passage, describe what you see as Voltaire’s vision of human nature in…

In this satirical piece, the ridiculous nature of man is exposed. The philosophy Pangloss teaches Candide is that whatever happens, it is all for the best, and whatever happens, it is the “best of…

• TARTUFFE

In Tartuffe what specifically do you think Moliere’s contemporaries found so objectionable about…

I can answer the first part of your question which should help you with second part. It would be helpful for you to refer to eNotes’ historical context and introduction to help with a better…