Question: (a) Prove that arctan x + arctan y = arctan (b) Use the formula in part (a) to show that x + y 1- xy'

(a) Prove that arctan x + arctan y = arctanx + y 1- xy' xy # 1.

(b) Use the formula in part (a) to show that

x + y 1- xy' xy # 1.

Step by Step Solution

★★★★★

3.21 Rating (148 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a b tan arctan x arctan y tan ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Calculus 10th Edition Questions!

Q:

Refer to following Exercise. (a) Use the formula in part (d) to calculate the probability that the underdog wins the World Series when p = .6. (b) If the World Series consisted of more than seven...

Q:

In each part, use the formula in Theorem 1.4.5 to compute the inverse of the matrix, and check your result by showing that AA-1 = A-1 A = I. (a) A=

Q:

Use the formula in Exercise 83. If f (4) = 5 and f' (4) = 2/3, find (f -1 )'(5).

Q:

MAT 275 Laboratory 7 Laplace Transform and the Symbolic Math Toolbox In this laboratory session we will learn how to 1. Use the Symbolic Math Toolbox 2. Calculate the Laplace and Inverse Laplace...

Q:

#include using namespace std; int counter; int partition( int a [], int low , int high ) { int x = a [ low ]; bool highTurn = true ; while ( low = x ) high --; else { a [ low ++] = a [ high ];...

Q:

Part II. Long Questions (50 marks) Write all your solution to the questions of this part in the answer book provided separately. For full credits, you should give concise and precise reasoning to...

Q:

For this question, please refer to code pasted at the bottom. In class we derived a formula for the number of item comparisons performed by quicksort in the best case, when the array size is a power...

Q:

Math 180 Practice Midterm #l l. A triangle has an unknown base b and height h. We know thta the hypotenuse is 30. Find a formula for the area in terms of the base I). 2. Find the domain of the...

Q:

please answer Problem # : (3 points childsmath, 7 points crowdmark) Determine the following limits. Show your work on Crowdmark and select the corresponding final answer for each part below. (a) lim...

Q:

For this question, please refer to code pasted at the bottom. In class we derived a formula for the number of item comparisons performed by quicksort in the best case, when the array size is a power...

Q:

Raymond wants to be sure that his life insurance policy will provide enough to take care of his wife and their four (4) kids. Raymond is 35 years old and sole provider in the family. He is currently...

Q:

QUESTION FOUR (15 MARKS) a) Let the national income model be given as Y = C + Io + G Cab(Y-To) G = gY (a > 0, 0

Q:

(a) In the celebrated case of Salomon v Salomon & Co Ltd [1897] AC 22, Lord Halsbury LC observed: Either the limited company was a legal entity or it was not. If it was, the business belonged to it...

Q:

Melissa Loester, the new controller of Power-Drives Inc., has just returned from a seminar on the choice of the activity level in the predetermined overhead rate. Even though the subject did not...

Q:

Suppose 70% of the cells are young. Consider again the cells in Section 6.4, Exercises 29 and 30, but suppose that older cells, instead of not staining as often, do not stain as well. In particular,...

Q:

Suppose Pr(cell is 0 day old) = 0.4 Pr(cell is 1 day old) = 0.3 Pr(cell is 2 days old) = 0.2 Pr(cell is 3 days old) = 0.1. Consider again the cells in Section 6.4, Exercises 31 and 32, but suppose...

Q:

Experiment c. For the data presented in Section 6.6, Exercises 1-4, write the results in terms of a random variable and find the expectation. What fraction of experiments have a result less than the...

Q:

please help with ones that say (select) too 1. preferred/common 2. equal/ uneven 3. equal/ uneven 4. net of future value(nfv)/ internal rate of return(irr)/ net of present value(npv) 5. nfv/irrpv...

Q:

An investment offers a total return of 16 percent over the coming year. Jerome Dowell thinks the total real return on this investment will be only 12 percent. What does Jerome believe the inflation...

Q:

Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $85,000 or $345,000 with equal probabilities of 0.5. The alternative risk-free investment in T-bills...