Math trig proofs... need help soon!?
3cos2x + 4sin 2x = 3(cos^2-sin^2x) + 4*2cosxsinx =3cos^2 - 3sin^2x + 8cosxsinx =(3cosx-sinx)(cosx +3sinx) 2sinxcosx = sqrt(2)cosx 2sinxcosx - sqrt(2)cosx =0 cosx(2sinx-sqrt(2))=0 cosx=0 x=npi+pi/2 rad (n any integer) or 2sinx-sqrt(2) = 0 2sinx = sqrt(2) sinx=1/sqrt2 x=(2n+1)pi +- pi/4 cos3xcosx + sin3xsinx -1 = cos(3x-x) - 1 =cos(2x) - 1 =1 - 2sin^2x -1 =-2sin^2x Assume -2sin^2x = 2cos(x)^2 cos^2x+sin^2x=0 but this is not true for any x cos^2x+sin^2x = 1 for all x
Need help with mathematical proof?
i have to say that the answer before me is proof that children these days haven't learned the proper way of using their head. Heed my advice steve g.... You are given a bird, an avian mammal capable of flight.... now say this bird flies into the president of the united states of america, and kills him, a paper will be published the following day and the bird will be mentioned in the news, for the bird is the news in this way, the bird is the word..... however nothing is certain.... peter griffin made a bold statement
Need help in mathematical proof?
I assume v is a unit vector. Since Dvf(a) exists, we have Dvf(a) = (del)f(a)*v, where "del"is the vector differential operator and * is the dot product. It follows that D-vf(a) = (del)f(a)*(-v) = -(del)f(a)*v = -Dvf(a).
Math proof help? please help?
1. Quad PQRT; QV bisects RT; QR || PV; PT = TV (Reason: Given) 2.
Mathematical proof, I REALLY NEED HELP!!!?
To show that R is an equivalence relation we must show that it is reflexive, symmetric, and transitive: 1. It is reflexive. For any integer a, 5a = 3a + 2a Ξ 0 + 2a = 2a. 2. It is symmetric. For any integers a and b suppose aRb. Then 5b Ξ 2b (by reflexivity) Ξ 5a (by hypothesis) Ξ 2a (by reflexivity) Thus 5b Ξ 2a (mod 3), proving that R is symmetric. 3. It is transitive. For any integers a, b, and c suppose aRb and bRc. Then 5a Ξ 2b (by hypothesis) Ξ 5b (by reflexivity) Ξ 2c (by hypothesis) Thus 5a Ξ 2c, so aRc, proving that R is transitive. --- Edited to clean up the equations a bit.
Could anyone help me solve these 2 math proofs?
[(sec x - tan x)^2 +1] / (secx cscx- tanx cscx) = 2 tan x LHS> = [(sec x - tan x)^2 +1] / cscx (secx - tanx) writing csc x = 1/sin x = [sin x (sec x - tan x) + [sin x /(secx - tanx)] trick for denominator of 2nd term> = [sin x(secx - tanx)+[sin x (secx+tanx)/(secx-tanx)(secx+tanx)] = [sin x(secx - tanx)+[sin x (secx+tanx)/(sec^2 x - tan^2 x)] = [sin x(secx - tanx)+[sin x (secx+tanx)/(1)] = [sin x(secx - tanx) + sin x (secx+tanx) = 2sin x secx = 2 tan x = RHS proved =================== (cscx + cotx)/ (tanx + sinx) = cotx cscx LHS> = (cscx + cotx)/ (tanx + sinx) = (1/sinx + cosx/sinx) / (sinx/cosx + sinx) = [(1 +cosx)/sinx ] /sinx) / [sinx (1+cosx)/cosx] cancelling (1+ cosx) = [1/sinx ] / [sinx /cosx] = cscx / tanx = cscx cotx
Maths proof help - multiple of 5?
This is if and only if so there are two statements here. 1) if n is a multiple of 5, then n^2 is a multiple of 5 2) if n^2 is a multiple of 5, then n is a multiple of 5 Proof of 1) Let n be a multiple of 5. Then 5 | n. Then there exists a number k such that 5k = n. Need to show n^2 is a multiple of 5. Need to show 5 | n^2. Need to find a number l such that 5l = n^2. Take 5k = n and multiply both sides by n 5k*n = n*n 5kn = n^2 Let l = kn. Then 5l = n^2 so 5 | n^2. Thus, n^2 is a multiple of 5 as needed. This proves 1). Proof of 2) Let n^2 be a multiple of 5. Then 5 | n^2. Then there exists a number k such that 5k = n^2. Note that any multiple of 5 must end in a 5 or 0. Since n^2 = n*n, clearly n and n have the same last digit. What two same digits mulitplied together gives us a 5 or 0. Check 0*0 = 0 1*1 = 1 2*2 = 4 3*3 = 9 4*4 = 16 (last digit 6) 5*5 = 25 (last digit 5) 6*6 = 36 (last digit 6) 7*7 = 49 (last digit 9) 8*8 = 64 (last digit 4) 9*9 = 81 (last digit 1) Thus, n must end in a 5 or 0. If n ends in a 5, then n = 10x + 5 for some integer x. Then n = 5(2x+1) so 5 | n. If n ends in 0, then n = 10x for some integer x. Then n = 5(2x) so 5 | n. Thus, n is a multiple of 5. We are done!
Math foundations proof! Help!?
Im going to help you out with the first one: 2a - 1 = 2a - 2 + 1 (subtract and add 1) = 2(a - 1) + 1 = 2j + 1, where j = a - 1, an integer. And so therefore, 2a - 1 is an odd integer, by the definition of odd. For the second one: n^2+n = n (n+1) Since either n or n+1 should be even, n (n+1) must be even so n^2 + n is even. And then the number + three is an odd number...So there ya go!
Which is the best book/course to help me with math proofs? I'm really bad at it. I've just got accepted to a PhD program in finance, and I need to improve that part.
During the two weeks before the first semester of the PhD in Economics program at Michigan State University, the department holds a Math Camp to help prepare incoming students. The book they use to teach proof technique and process is How to Prove It: A Structured Approach, 2nd Edition: Daniel J. Velleman.I emphatically recommend this book! Check out the Amazon reviews. You can find solutions for free online, but be critical of these. There is also an official solution manual, I believe.Mathy folks repeat this next point ad nauseum, but do the exercises! You will not learn a thing by reading this book — or any other higher-level math text for that matter — without also proving results for yourself.Good luck!
How can one prepare for a proof based mathematics course?
Georgetown University professor Cal Newport has a helpful guide on tackling a proof-based class (Case Study: How I Got the Highest Grade in my Discrete Math Class). I'm quoting the main part of his article below. Click to the webpage for the entire story.Discrete math is about proofs. In lecture, the professor would write a proposition on the board — e.g., if n is a perfect square then it’s also odd— then walk through a proof. Proposition after proposition, proof after proof. As the class advanced, we learned increasingly advanced techniques for building these proofs. I soon developed a singular obsession: I wanted to be able to recreate, with pencil and paper, and no helper notes, every single proof presented in class. No exceptions. Lack of understanding of even one proof wouldn’t be tolerated.My Obsession in PracticeHere’s how I learned every proof.I bought a package of white printer paper.As the term progressed, I copied each proposition presented in class onto its own sheet of paper. I would write the problem as the top of the sheet and recreate the proof, from my notes, below.I tried to do this every week — copying the most recent material onto its own sheets — though I often got behind.While doing this work I would sometimes — okay, many times — realize I didn’t quite understand the proof I had copied in my notes. In these cases, I would break out the textbook, or do some web searching for the problem, to see if I could make sense of what I was writing down. This usually worked. In the worst case scenario, I would ask the professor or the TA for help. Not understanding the proof was not an option. I wasn’t practicing transcription; I knew I had to learn these.About two weeks before each exam I started scheduling sessions to aggressively review my “proof guides.” I always worked on the second floor of the Dana Biomedical Library on the outskirts of campus. (Think: dark, concrete-floored stacks, with desks tucked away at then end of long rows, each illuminated by a single, bright incandescent bulb…study heaven.) I did standard Quiz and Recall: splitting the proofs between those I could replicate from scratch and those that gave me trouble, and then, in the next round, focusing only on those that gave me trouble, and so on, until every sheet had been conquered.By the day of the exam, you could give me any problem from the course and I could rattle off the proof, without mistake and without hesitation.