Identity Definition and 1000 Threads

Homework Statement tanx=csc2x-cot2x Homework Equations Quotient, Reciprocal, Pythagoreans The Attempt at a Solution 1/sinx + 1/sinx - cosx/sinx - cosx/sinx = 2/sinx - 2cosx/sinx = (2-2cosx)/sinx STUCK~

Homework Statement Let f(x,y,z)=0 and r=r(x,y,z) be another constraint. show that if r is held constant then (\partial x/\partial y)_r *(\partial y/\partial z)_r *(\partial z/\partial x)_r = 1 hint: consider dr and use the fact: (\partial x/\partial y)_z *(\partial y/\partial...

Homework Statement Use the Summation Identity to count the cubes of all integers sizes formed by an n by n by n assembly of cubes. Homework Equations Summation Identity: Sum [from i = 0 to n] (i choose k) = (n+1 choose k+1). Sum [from i = 0 to n] (i^3) = (n^2)(n+1)^2 / 4 = (sum[from...

Homework Statement required to prove: (\nabla^2+k^2)\frac{e^{ikr}}{r}=-4\pi\delta (r) Homework Equations im assuming we are working in spherical coordinates (not sure - could be cylindrical/2D polar) laplacian for spherical (considering its only a function of r) is...

Homework Statement Verify that \frac{Csc(x)}{Cot(x)+Tan(x)}=Cos(x) is an identity. Homework Equations All of the trigonometric identities. Sin^{2}+Cos^{2}=1; tan^{2}+1=Sec^{2}; 1+Cot^{2}=Csc^{2}; etc. The Attempt at a Solution I've literally written about five pages worth trying...

Hey all, hope you could help me, would be very gratefull if you could. Homework Statement Show that sin(x) + cos(x) = √2sin(x + π/4) Homework Equations sin(x+z) = sin(x)cos(z)+sin(z)cos(x) The Attempt at a Solution Ive been doing some of these trig identity problems without an...

Hello everyone, i was checking out a paper on simple rings http://www.imsc.res.in/~knr/RT09/sssrings.pdf and they said that all commutative simple rings are fields. i just don't see why they should have identity. thank you.

Homework Statement u and v are vectors Homework Equations show that : mod(u x v)^2 +(u.v)^2 = mod(u)^2 x mod(v)^2 The Attempt at a Solution I thought about let u =(a,b,c) let v = (x,y,z) and then doing the calculations. However I have done this but then squaring everything out...

This is a question about Ward-Takahashi Identity.I go through the materials presented about Ward Identity in Peskin's book. there are two sections where mentioned this identity. First, in section 5.5, when the author discussed photon polarization sums. Second, in section7.4, where the author...

Homework Statement In order to solve the problem I am working on, I have to prove the following generalized problem, S(x)=\sum_{n=0}^{\infty} n x^n =\frac{x}{(x-1)^2} for |x|< 1 I evaluated this sum using Wolfram Alpha. Clearly it looks related to the geometric series solution, but I am...

Do somebody knows anything about the Dirca's identity? \begin{equation} \label{Dirac} \frac{\partial^2}{\partial x_{\mu}\partial x^{\mu}} \delta(xb_{\mu}xb^{\mu}) = -4\pi \delta(xb_0)\delta(xb_1)\delta(xb_2)\delta(xb_3) \end{equation} here xb, is the 4-vector $x-b$ in Minkowsky spacetime...

Hey folks! I'm trying to figure out an identity from a paper on dimensional regularization. Here's the identity: -\frac{1}{2}\frac{d}{ds}|_{s=0}\int_0^\infty \frac{d^4k}{(2\pi)^4}(k^2+m^2)^{-s} after performing the k-integral this becomes...

Is it true that for all antisymmetric tensors F^{\mu\nu} the following identity is true: \nabla_\mu \nabla_\nu F^{\mu\nu}=0 (I've checked it but I'm not absolutely sure).

Homework Statement sin (x) + sin (3x) + sin (5x) + sin (7x) = 4cos(x)cos(2x)sin(4x) Homework Equations sin(a+b)=sin(a)cos(b)+sin(b)cos(a) sin(a-b)=sin(a)cos(b)-sin(b)cos(a) The Attempt at a Solution Me and four of my classmates have tried to do this proof and it kicked our ***...

vector identity?? Homework Statement The text that I'm reading has a line that reads \left(\mathbf{b}\mathbf{k}\cdot-\mathbf{b}\cdot\mathbf{k}\right)\mathbf{v}=\omega\mathbf{B} and I'm not sure what it means by \mathbf{b}\mathbf{k}; it's clearly not the dot product nor the cross product. A...

This is crazy. I have no idea what the textbook is saying at the end. So far, so good. Then this flies at me out of nowhere: We do?? Where the hell did that come from? I've never stared at something for so long without having the slightest clue what is going on. I held up the whole class...

Does x & y directions commute? Seem trivial! Just wondering whether any measurement made in the x direction affect it's y coordinate.

Homework Statement tan^2(x/2)=(sec x-1)/(sec x+1) Homework Equations The Attempt at a Solution

Homework Statement For two waves in superposition, we have, let say \[y_{1} = Asin(kx-wt), y_{2} = Asin(kx-wt+\Phi )\] We use the trig identity sin A + sin B to simplify the combination Whereas for standing waves, we use the trig identity sin(a +/- b) to combine the result. As I...

Are there any identities that are true for all real numbers, but not for all complex numbers? The only one I can think of is... \sqrt{ab}=\sqrt{a}\sqrt{b} Which is only true if a and b are POSITIVE, not real. But is there any identity that works for all real numbers, but fails for complex...

Homework Statement Prove the following identity: e^{x \hat A} \hat B e^{-x \hat A} = \hat B + [\hat A, \hat B]x + \frac{[\hat A, [\hat A, \hat B]]x^2}{2!}+\frac{[\hat A,[\hat A, [\hat A, \hat B]]]x^3}{3!}+... where A and B are operators and x is some parameter. Homework Equations...

Homework Statement Using index notation to prove \vec{\nabla}\times\left(\vec{A}\times\vec{B}\right) = \left(\vec{B}\bullet\vec{\nabla}\right)\vec{A} - \left(\vec{A}\bullet\vec{\nabla}\right)\vec{B} + \vec{A}\left(\vec{\nabla}\bullet\vec{B}\right) -...

Hi, I'm working my way through Schwinger's paper (http://www.physics.princeton.edu/~mcdonald/examples/QED/schwinger_pr_82_664_51.pdf" ) and I came across the following identity -(\gamma\pi)^2 = \pi_{\mu}^2 - \frac{1}{2}e\sigma_{\mu\nu}F^{\mu\nu} where \pi_{\mu} = p_{\mu} - eA_{\mu}...

let m,n be positive integer. Prove the identity: sum (i from 0 to k): { C(m, i) * C(n, k - i) } = C(m + n, k) Hint: Consider the polynomial equation: sum (k from 0 to m+n) {C(m + n, k) *z^k } = (1 + z)^(m+n) = ((1+z)^m) * ((1+z)^n) I tried long time, still have no idea.

Consider a binary operation on a set G. A an element e of G is said to be a left identity if ex=x for all x. If x is in G, an element y of G is said to be a left inverse of x if yx is a left identity. A right identity and right inverse is defined similarly. Is the following an adequate...

I've been asked by my professor to identify a group of singular matrices. At first, I did not think this was possible, since a singular matrix is non-invertible by definition, yet to prove a groups existence, every such singular matrix must have an inverse. It has been brought to my...

Can anyone provide me solution to this identity http://books.google.com/books?id=PJeHprppOLsC&printsec=frontcover&dq=complex+variables&hl=en&ei=rFl7TMj0E4P-8AbNgOGFBw&sa=X&oi=book_result&ct=book-thumbnail&resnum=2&ved=0CDYQ6wEwAQ#v=onepage&q&f=false" page 10 , problem 20

Hello, I was looking at some math problems and one kind caught my attention. The idea was to prove that let's say 3x+2y=5 has infinitely many solutions over the integers. Can someone show me the procedure how a problem like this might be solved?

Harmonic function satisfies Laplace equation and have continuous 1st and 2nd partial derivatives. Laplace equation is \nabla^2 u=0. Using Green's 1st identity: \int_{\Omega} v \nabla^2 u \;+\; \nabla u \;\cdot \; \nabla v \; dx\;dy \;=\; \int_{\Gamma} v\frac{\partial u}{\partial n} \; ds...

Homework Statement Attached question Homework Equations The Attempt at a Solution The second part of question is relatively easy, it is the first part of the question where I need help with(using arg zw = arg z + arg w to show arg z^n = n arg z). Also, is the question asking...

Help! I spent 3 hours attempting this question. Prove the following identity : (tan x + sec x -1) / (tan x - sec x + 1) = tan x + sec x I've simplified Left Hand Side into cos and sine. Which ended up like this (sine x - cos x + 1) / (sine x + cos x -1) Then I'm stuck. Any help is...

what do u think of people who have face identity? are they liar or sick? can u trust them? it happens on net a lot that people introduce themselves somebody else. some of them try to impress others by telling lies but i know of so many people who just tell lies about their names...

Homework Statement So we have an observable K = \begin{bmatrix} 0 & -i \\ -i & 0 \end{bmatrix} and its eigenvectors are v1 = (-i, 1)T and v2 = (i, 1)T corresponding to eigenvalues 1 and -1, respectively. Now if we take the outer products, we get these... |1><1| = (-i, 1)T*(i, 1) =...

Homework Statement sin(4x) = 8cos3(x)sin(x)-4sin(x)cos(x) Homework Equations All trigonometric identities The Attempt at a Solution I can simplify the right side using the double angle identity to: sin(4x) = 4sin(2x)cos2(x)-2sin(2x) However, now I'm not sure what to do. Did...

A lot has been discussed/posted about various models/theories to explain consciousness, the systems of laws, fundamental physics, emergence, upward and downward causality etc. However I think too much of these theories focus on GENERAL universals and ultimately on the mechanisms, but not on...

Just wondering how this is simplified to the third line: If w, z are complex numbers wz = rs( cos\alpha + isin \alpha ) (cos \varphi + isin \varphi) wz = rs(cos\alpha cos \varphi - sin \alphasin\varphi) + i(sin \alphacos\varphi + cos \alpha sin \varphi)) wz = rs(cos (\alpha...

Does anyone know how to prove the following identity: \Sigma_{k=0}^{n}\left(\stackrel{n}{k}\right) H_{k}(x)H_{n-k}(y)=2^{n/2}H_{n}(2^{-1/2}(x+y)) where H_{i}(z)represents the Hermite polynomial?

Hi, I start with arctanh\left(\frac{A}{\sqrt{A^2-1}}\right)=\frac{1}{2}ln\left( \frac{1+\frac{A}{\sqrt{A^2-1}}}{1-\frac{A}{\sqrt{A^2-1}}}\right) The function \frac{A}{\sqrt{A^2-1}} is real, and since A>1, it too is always greater than 1. Is it true that it should really be the modulus...

1. By considering, seperately, each component of the vector A, show that \iint A(u.n) ds = \iiint {(u.\nabla)A + A(\nabla.u)} dV (A,u and n are vectors) Homework Equations 3. Attempt at solution L.H.S. Let A = a\vec{i} + b\vec{j} + c\vec{k} \iint (a\vec{i} +...

1. By considering each component of the vector A show that \iint A(u.n)ds = \iiint{(u.nambla)A+A(nambla.u)}dV (A,u and n are vectors) Homework Equations 3. Let A = ai + bj + ck. L.H.S: \iint ai (u.n)ds + \iint bj (u.n)ds +\iint ck (u.n)ds R.H.S. = \iiint(u.nambla)ai dV+...

Is there a shorter way to verify this identity, as you can see I haven't even finished it. I know you can use Ven diagrams and truth tables but I wanted to avoid them inorder to use a more general formal approach. picture is attached

Hello everyone, I would like to ask what's the purpose of identity map? Recently I came across something that apparently use this to find the inverse image of a function F(x) in the form of F(x) = ( f(x) , x ) . Thanks. Wayne

Homework Statement Show using Stoke's Theorem that S is an open surface with boundary C (a space curve). f(\vec r) is a scalar field. Homework Equations Stoke's theorem \iint_S (\nabla\times \vec F) \cdot d\vec S = \int_C F \cdot d\vec r The Attempt at a Solution Thus far...

Homework Statement I did the question with help, but did not understand why did we multiply e^-i(x/2) How do I know what to multiply for getting the real part of a complex number in exponential form? Homework Equations The Attempt at a Solution

Hello, Could you please clarify if this is correct: If tan^(-1)(x) = Pi/2 - tan^(-1)(1/x) Then if we have (ax) as the angle where a is a constant, do we get: tan^(-1)(ax) = Pi/2 - tan^(-1)(a/x) or does the constant go on the bottom with the x? i.e. or: tan^(-1)(ax) = Pi/2 -...

Hi. I'm having trouble trying to understand the relationship between inverse trig functions, especially arcsin x, and pythagorean identity. I know that because cosx=sqrt(1-(sinx)^2), derivative of arcsin x is 1/(cos(arcsin x)) = 1/(sqrt(1-(sinx)^2)arcsinx)) = 1/(sqrt(1-x^2). But how does...

http://www.identitytheft.com/article/are_photocopiers_a_risk

Homework Statement map the function \begin{equation}w = \Big(\frac{z-1}{z+1}\Big)^{2} \end{equation} on some domain which contains z=e^{i\theta}. \theta between 0 and \pi Hint: Map the semicircular arc bounding the top of the disc by putting $z=e^{i\theta}$ in the above formula. The...

Homework Statement Let \mathbf{G}(x,y,z) be an irrotational vector field and g(x,y,z) a C^1 function. Use vector identities to simplify: \nabla\cdot(g\nabla \times (g\mathbf{G})) Homework Equations The '14 basic vector identities' The Attempt at a Solution I tried using the...

Homework Statement Let F(x,y,z) be an irrotational vector field and f(x,y,z) a C^1 scalar functions. Using the standard identities of vector analysis (provided in section 2 below), simplify (\nabla f \times F) \cdot \nabla f Homework Equations Note: The identities below require...