identities Definition and 416 Threads

Homework Statement Prove cot(x) - tan(x) = 2tan(2x) Homework Equations Trig identities http://en.wikipedia.org/wiki/List_of_trigonometric_identities The Attempt at a Solution I have worked it down and don't think they are equal. I think it's supposed to be 2cot(2x) not 2tan(2x)...

I must become good at this ASAP. Homework Statement prove \vec{\nabla}\cdot (\vec{a}\times\vec{b} ) = \vec{b} \cdot(\vec\nabla\times\vec{a}) - \vec{a}\cdot(\vec\nabla\times\vec{b}) Homework Equations \vec a \times \vec b = \epsilon_{ijk}\vec a_j \vec b_k \vec\nabla\cdot =...

Homework Statement use trig identities to show that (b) cos(tan^(−1)[x])=1/√(1+x^2) for −1/2π<x<1/2π. Homework Equations i think Pythagoras has to applied but that is geometric reasoning hmm The Attempt at a Solution

Homework Statement Prove that cotx-tanx=2cot 2x Homework Equations Is 2cot 2x the same as 2(cos2x/sin2x) The Attempt at a Solution

Hi All, I am struggling to prove the following identity $$ 1 + y + \frac{1}{2!}y^2 + \frac{1}{3!}y^3 + \dots = lim_{N \to \infty} \sum_{r=0}^{N} \frac {N!}{r! (N-r)!} \frac{y}{N}^{r} = lim_{N \to \infty} (1 + \frac{y}{N})^N $$ any hint would the most appreciated. I understand the...

Hey! :o I am looking at the identities of the optimal approximation. At the case where the basis consists of orthogonal unit vectors,the optimal approximation $y \in \widetilde{H} \subset H$, where $H$ an euclidean space, of $x \in H$ from $\widetilde{H}$ can be written $y=(x,e_1) e_1 +...

Homework Statement Which is equivalent to: cos(∏/2 + x) - cos(∏/2 - x)? A) -2cos(x) B) -2 C) 0 D)-2sin(x) Homework Equations Cos (A-B) The Attempt at a Solution I am totally stuck :( please help!

It is surprising how expensive the books are that contain the Ramaujan identities and equations. I understand the work to 'prove' them must have been a tremendous undertaking however I find the price of the 'notebooks' for Ramanujan's work prohibitively expensive. I believe wolfram put it...

I am looking for a book that has a comprehensive list of Ramaujans Identities and Equations. I have read that he created 3900 such pieces of work and it would be fascinating to see such a collection that came from just one person.

A little confused on something. Suppose I have the integral $$2 \int 4 \sin^2x \, dx$$ So I understand that $$\sin^2x = \frac{1 - \cos2x}{2}$$ BUT we have a 4 in front of it, so shouldn't we pull the $$4$$ out in front of the integral to get: $$8 \int \frac{1 - \cos 2x}{2} \, dx$$ then...

I have a hard time believing we only have the limited number of series I have seen so far especially considering how much broader mathematics is than I had thought just a short while ago. Where should I search to find more infinite series summations for the gamma function? For example which...

If I have some new identities that are very powerful but don't have time to go into the details is it okay to simply post just the functions on arXiv for now? A quick check on wolfram as to the validity of the functions will confirm all my work.

This is one of the example problems in my book to show how to deal with integrating trigonometric functions to higher powers, by breaking them down into identities. $$=\int cos^5x dx$$ $$=\int (cos^2x)^2cos^x dx $$ $$=\int (1-sin^2x)^2*d(sin x)$$ $$=\int (1-u^2)^2 du$$ $$=\int 1-2u^2 + u^4...

Homework Statement prove using the compound angle identies, proove the following: \frac{sin(A-B)}{cos(A)cos(B)}+\frac{sin(B-C)}{cos(B)cos(C)}+\frac{sin(C-A)}{cos(C)cos(A)}=0 Homework Equations n/aThe Attempt at a Solution I resolved it to...

Homework Statement If ##\sec x-\csc x=\pm p##, show that ##p^{2} \sin^2 2x +4\sin 2x-4=0## Show conversely that if ##p^{2} \sin^2 2x +4\sin 2x-4=0##, then ##\sec x-\csc x## is equal to +p and -p. Find, to the nearest minute, the two values of x in the range of 0 to 360 degrees, the equation...

Found out that: 1/(1-x) = the infinite product of (1+x^(2^N)) from N=0 to infinity. From "The Harper Collins Dictionary of Mathematics" by Borowski and Borwein. Makes me wonder whether this identity could be used to make some complex algebraic manipulations into real manipulations...

Here is the question: I have posted a link there to this thread so the OP may view my work.

Vector differential identities! In chapter 20 of "Foundations of Electromagnetic theory" by Reitz,Milford and Christy,there is calculation which seems to make use of: \vec{\nabla}\times\dot{\vec{p}}=\Large{\frac{\vec{r}}{r}\times\frac{ \partial \dot{\vec{p}}}{\partial r}} where...

Hey! :) I need some help at the following exercise: Let v_{1}, v_{2} solutions of the differential equation y''+ay'+by=0 (where a and b real constants)so that \frac{v_{1}}{v_{2}} is not constant.If y=f(x) any solution of the differential equation ,use the identities of the Wronskian to show...

I have an vector calculus identity to prove and I need to use vector notation to do it. The identity is $$\vec{\nabla}(fg)=f\vec{\nabla}{g}+g\vec{\nabla}{f}$$ I tried starting with the left side by writing $\vec{\nabla}(fg)=\nabla_j(fg)$. Now I look and that and it really looks like there is...

Hello there, I am struggling in proving the following. The principle of Minimum energy for an elastic body (no body forces, no applied tractions) says that the equilibrium state minimizes $$\int_{\Omega} \nabla^{(s)} u D (\nabla^{(s)}u)$$ among all vectorial functions u satisfying the...

Proving Some Poisson Bracket identities -- a notational question I need some help just understanding notation, and while this might count as elementary it has to do with Hamiltonians and Lagrangians, so I posted this here. Homework Statement Prove the following properties of Poisson's...

hey all! i was hoping someone could either state an article or share some knowledge with a way (if any) to derive the vector calculus "del" relationships. i.e. $$ \nabla \cdot ( \rho \vec{V}) = \rho (\nabla \cdot \vec{V}) + \vec{V} \cdot (\nabla\rho)$$ now i do understand this to be like...

Does anyone know if there is a good place to find a list of proof identities? Basic stuff like the disjoint or if-then in logic symbols. It would be nice to have a place to make sure I'm remembering them correctly and to search for more. Thanks!

Homework Statement How to quickly solve problems on maximum and minimum values of trig functions with help of calculus: Ex. 10cos2x-6sinxcosx+2sin2xHomework Equations noneThe Attempt at a Solution I know the method of simplification. But i want to do it quickly with calculus. How to do that??

I've got this problem right now, which asks me to prove that $$Ccos(\omega_{o}t-\phi)=Asin(\omega_{o}t)+Bcos(\omega_{o}t)$$ This proved to be a bit more difficult than I expected, so I looked up a complete list of trig identities. $$cos(a\pm{b})=cos(a)cos(b)\mp{sin(a)sin(b)}$$ seems like the...

I am having trouble establishing a process to verify various identities for problems in index notation. Description of Problem Verify that \epsilon_{ijk}\epsilon_{iqr}=\delta_{jq}\delta_{kr}-\delta_{kq}\delta_{jr} Attempt at Solution I know that the term is only positive if there is an...

I'm having some confusion with a couple trig identities. On wikipedia (http://en.wikipedia.org/wiki/List_of_trigonometric_identities#Product-to-sum_and_sum-to-product_identities), the following two identities are listed: sinθcosβ = (1/2)[sin(θ+β) + sin(θ-β)] and sinβcosθ =...

Homework Statement I want to derive the trig identities starting with rotation on the plane. Homework Equations One rotation through a given angle is given by $$x' = xcosθ - ysinθ $$ $$y' = xsinθ + ycosθ$$ The Attempt at a Solution What if I wanted to rotated through any...

Hi guys!I have a question..How can I show that the function that has the following identities: \bullet f(x)\neq 0 ,x\in\mathbb{R}. \bullet f(0)=f\left(\dfrac{2}{3}\right). \int_{0}^{x}\frac{f(t)f(x-t)}{f(\frac{2+t}{3})f(\frac{2+x-t}{3})}=\int_{0}^{x}\frac{f^2{(t)}}{f^2{(\frac{2+t}{3}})} is...

I can find for example Tan(2x) by using Euler's formula for example Let the complex number Z be equal to 1 + itan(x) Then if I calculate Z2 which is equal to 1 + itan(2x) I can find the identity for tan(2x) by the following... Z2 =(Z)2 = (1 + itan(x))2 = 1 + (2i)tan(x) -tan(x)2 = 1...

Homework Statement Prove that the two trig identities are equivalent. cos \ x \ -\frac{cos \ x}{1-tan \ x} \ = \ \frac{sin \ x \ cos \ x \ }{sin \ x \ - \ cos \ x} The Attempt at a Solution My professor recommended that we only work with one side of the equality when we're trying...

Homework Statement Determine the general solution of: y(6) + y''' = t The Attempt at a Solution Ok, r = 0, 0, 0, 1/2 +- 3i/√2, -1/2 + 3i/√2 What do I do with that last r value? It turns into ce-t somehow, but I don't see it. edit: typed a number in wrong, fixed now~

Homework Statement Prove the following identities 31c) sin(\frac{\pi}{2}+x)=cosxHomework Equations sin2x+cos2x=1 The Attempt at a Solution The idea here is to prove the identity by making LS=RS so here is what i have done, but I am not sure if it is the right way, since the book shows it...

Given: A + B + C = 180 degrees Prove: TanA + TanB + TanC = TanA x TanB x TanC First time submitting something. Thank you all.

Hi everybody, I am just trying to find a decent identity that relates the sum $$\sum_{k=0}^{n}a_kb_k$$ to another sum such that ##a_k## and ##b_k## aren't together in the same one. If you don't know what I mean, feel free to ask. If you have an answer, please post it. Thanks in advance!

Homework Statement Proof that (1/6)sin(3x)-(1/18)sin(9x) = (2/9)sin^3(3x) Homework Equations The Attempt at a Solution I am just curious exactly how the power on the sine function is cubic on one side. It obviously has to do with something that increases the power on the...

Prove two integral identities? 1. The following integral identity holds \dfrac{d}{dx}\intop_{x}^{a}\dfrac{F(\rho)d\rho}{\sqrt{\rho^{2}-x^{2}}}=-\dfrac{F(a)x}{a\sqrt{a^{2}-x^{2}}}+x\intop_{x}^{a}\dfrac{d\rho}{\sqrt{\rho^{2}-x^{2}}}\dfrac{d}{d\rho}\left[\dfrac{F(\rho)}{\rho}\right] Hints: this...

HI, does anyone know a decent site where I can find a few product identities? I googled it, but all that came up were trig identities. I am not looking for those; I am specifically looking for product of a sequence identities: ∏

Homework Statement I understand this chapter a little better than the previous ones, but I'm having problems with these two problems. Can anyone at least lead me in? Homework Equations The Attempt at a Solution Starting from the right side for both. For the second one, turning the...

Homework Statement Use the figure to evaluate the function that f(x)=sin(x) f(θ/2) Homework Equations n/a The Attempt at a Solution x2+y2=1 x= -2/7 (-2/7)2+y2=1 y=√(6)/7 sin(θ/2)= +/- √(1-cos(θ)/2) (the whole function is over 2 inside of the square root) =+/-...

Homework Statement Prove the following: tan2A=2tanA/1-tan^2A Homework Equations The Attempt at a Solution Took the right hand side: =2(sinA/cosA) / 1-(sin^2A/cos^2A) =2sinA/cosA /cos^2A-sin^2A/cos^2A =2sinA/cos2A /cosA/1 Dont know what to do next?

Here is the question: Here is a link to the question: Pre-calc math problem? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement If A and B are events, use the axioms of probability to show: a) If A \subset B, then P(B \cap A^{C}) = P(B) - P(A) b) P(A \cup B) = P(A) + P(B) - P(A \cap B) Homework Equations Axiom 1: P(x)\geq 0 Axiom 2: P(S) = 1, where S is the state space. Axiom 3: If...

Homework Statement I just have to prove the well known identities: \cos(\alpha + \beta)=\cos(\alpha)\cos(\beta)-\sin(\alpha)\sin(\beta) \sin(\alpha + \beta)=\sin(\alpha)\cos(\beta)+\cos(\alpha)\sin( \beta) But the thing is that I've to use the Taylor power series for the sine and cosine...

Homework Statement a) Derive Green's identities in local and integral form for the partial differential operator ##\triangle^2##. b) Compute the adjoint operator ##(\triangle^2)^*##. 2. Relevant information ##U\subset\mathbb{R}^n##, ##u:U\to\mathbb{R}##, differential operator ##Lu##. In...

Homework Statement Show, using complex numbers, that sin(x)+cos(x)=(√2)cos(x-∏/4) Homework Equations cos(x)=(e^(ix)+e^(-ix))/2 sin(x)=(e^(ix)-e^(-ix))/2i e^ix=cos(x)+isin(x) The Attempt at a Solution I was given the hint that sin(x)=Re(-ie^(ix)), but have thus far not been...

Hi I am in need of some help for this question: 1+tanx/1-tanx = tan(x+(∏/4)) It is easy to solve with the tan trig identites on the right side however, my teacher had told me to do it with SIN and COS only. I am not sure if its possible and was looking for some insight Left Side...

Help with Double Angle Identities! cos θ = 24/25 The angle lies in quadrant 1; 0<θ<90 Find sin2θ I know you would use either the formula cos^2θ - sin^2θ or 2sinθcosθ And I know that the answer is 339/625, but I do not know how to get that answer?

Hey PF! Homework Statement Find exact solutions for the following equations over the domain 0 ≤ x <2π 2sinx = 3 + 2cscx Homework Equations sin2+cos2=1 The Attempt at a Solution 2sinx = 3 + 2cscx 2sinx = 3 +2(1/sinx) sinx = 3/2 + 1/sinx sinx - 1/sinx = 3/2 (1-1-cos2x)/sinx = 3/2 -cos2x/sinx =...