Identity Definition and 1000 Threads

I'm trying to do excercise 4.8 in "Riemannian manifolds" by John Lee. (It's about showing that the geodesics of \mathbb R^n are straight lines). The result I'm getting is that the definition of a geodesic implies the well-known identity 0=0, which isn't very useful. I must have made a mistake...

Hi, I was asked to prove this identity, I found the determinants for both the left and the right side, and now I basically have to prove that (d/dy)(f(dg/dz))=(df/dy)(dg/dz), the d's are actual partials though. Can anyone give me an idea on how to prove this? Thanks.

While seeing a signals example problem, I encountered this: cos^2 (wt+θ) = [1+cos(2wt+2θ)] What identity is this?

In Eq 11.72 in the QFT text by Peskin, the following equality is stated: i\int\frac{d^{d}k_{E}}{(2\pi)^{d}}\log(k_{E}^{2}+m^{2})=-i\frac{\partial}{\partial\alpha}\int\frac{d^{d}k_{E}}{(2\pi)^{d}}\frac{1}{(k_{E}^{2}+m^{2})^{\alpha}}|_{\alpha=0} This suggests that...

Hi, I am new with linear algebra, and I'm having a hard time wrapping my mind around the 0 vector and the additive identity v + 0 = v, where 0 is the 0 vector. If I had a 2x2 matrix, and v + w = C + (C^T)*D ... (where (C^T) is the transpose, v & w are vectors, and C & D are matrices)...

Could someone please explain to me in simple words (i.e., without referring to forms on the frame bundle, etc) why the Bianchi identity is the relativistic generalisation of the momentum-conservation law? Here comes my hypothesis, but I am not 100% convinced that it is correct. In Newtonian...

Homework Statement Let z=x+iy prove that Exp[z1]*Exp[z2]=Exp[z1+z2] Homework Equations Binomial thm (x+y)^n=Sum[Bin[n,k]*x^n-k*y^k,{k,1,n}] The Attempt at a Solution I have no idea about this question... Please give me some help.

Matrix A= 2x2, R1= -1, -1, R2= -7, 3 Matrix b= 2x2, R1= 1,0, R2= 0, 1 A*?=b ____________ To solve, I put ? on the one side of the equation as ?=A^(-1)b. My answer is then just the inverse of A, because what is multiplied by the identity matrix is itself. It is shown to be incorrect...

Hi friends, I am not able to understand how the below shown identity becomes (-1) power v cosθ. cos(vπ − θ ) = cos vπ cos θ + sin vπ sin θ = (−1)power v cos θ ==> (-1)vcos θ Please help me understand this basic problem. Thanks, Nesta

I have a simple technical problem. I'm following a paper [Shore, G. Ann Phys. 137, 262-305 (1981)], and I am unable to show a very simple identity for the non-abelian fluctuation operator (eq 4.37): D_\mu\left[-D^2\delta_{\mu\nu}+D_\mu D_\nu-2F_{\mu\nu}\right]\,\phi=-(D_\mu F_{\mu\nu})\,\phi ...

Hello, in a paper I have the identity \int_{-\infty}^{\infty} d x \sqrt{(x-i\epsilon)^2-1}= I_+ - I_- + i \int_{-1}^{1}(\ldots) where I_+ = \int_1^{\infty}(\ldots), I_=\int_{-\infty}^{-1}(\ldots) and \epsilon is a small positive number that will be taken to zero at the end. My...

Homework Statement Prove that the additive identity in a vector space is unique Homework Equations Additive identity There is an element 0 in V such that v + 0 = v for all v in V The Attempt at a Solution Assume that the additive identity is NOT unique, then there exists y...

interval from a to b \int f(x) dx = interval from b to a (-)\int f(x) dx Is this correct? Swapping the interval endpoints changes the sign of the integral? It seems like they should be equal. Thanks for the help. By the way, I saw this property here...

sin^2(x)-sin^2(2x)=cos^2(2x)-cos^2(x) I need help with proving this trig identity. Every thing I've tried just makes the problem more confusing. How would you guys go about this?

URGENT:trigonometric identity question Homework Statement tan2x+cos2x+sin2x=sec2x *the 2 stands for squared since I don't know how to make the squared symbol appear on a compter Homework Equations http://www.analyzemath.com/Trigonometry_2/Trigonometric_identities.html stuff from...

I know I haven't entered the formulae with the proper syntax, but I'm extremely exhausted at the time of posting, so please just read it and give advice, forgiving me this once for not using proper form (it's basically in latex code format). Homework Statement Show...

Homework Statement I'm a bit confused as to the following vector calculus identity: [∇ (∇.A)]_i = (δ/δx_i )( δA_j/δx_j) Shouldn’t it be = (δ/δx_i )( δA_i/δx_i) why is it ‘j’ if we are taking it over ‘i’ ? Thanks.

Homework Statement I'm supposed to verify this: \frac{cos(2x)-cos(4x)}{sin(2x)+sin(4x)}=tanx The attempt at a solution I reworked it every way I could think of, but it just won't work. I got desperate so I plugged it into some site and it said it was not a real identity, so I now I'm...

Homework Statement This is a problem from a textbook, Riley Hobson and Bence 'Mathematical Methods for Physics and Engineering'. It asks to check the validity of a vector identity. If a, b and c are general vectors satisfying a x c = b x c, does this imply c . a - c . b = c|a-b| 2. The...

Homework Statement sec^2(x) tan^2(x) + sec^2(x) = sec^4(x) Homework Equations sin^2 + cos^2 = 1 1+tan^2 = sec^2 1+cot^2 = csc^2 The Attempt at a Solution First, I changed everything to sin and cos to try and make it clearer. 1/cos^2 * sin^2/cos^2 + 1/cos^2 = sec^4...

I would like to demonstrate an identity with the [SIZE="4"]INDICIAL NOTATION. I have attached my attempt. Please let me know where I made mistakes. Any suggestion? I am trying to understand tensors all by myself because they are the keys in continuum mechanics Thanks

Homework Statement Hi all , again i am stuck onto this question :( , tried over 3 sheets alone on it lol.btw. thanks for your replies ;) . Prove the Identity (cosecA+cotA)^2 similar to 1+cosA/1-cosA Homework Equations hmm let's see.. sin2+cos2=1 , sec2= 1+tan2 cosec2= 1+cot2...

Homework Statement Use a graphing calculator to test whether the following is an identity. If it is an identity, verify it. If it is not an identity, find a value of x for which both sides are defined but not equal. \frac{cos(-x)}{sin(x)cot(-x)}=1 Homework Equations None The...

Homework Statement verify the following identity: Sec(x)Sin2(x) ______________________ = 1 - cos(x) 1 + sec(x) Homework Equations sec(x)=1/cos(x) sin2(x)=1-cos2(x) The Attempt at a Solution I never know how to start off these problems. I have to take the...

csc(theta) - sin(theta) = cos(theta)*cot(theta) I'm supposed to write a proof for this but to be honest I'm not really sure where I should even start. The prof taught to take one side of the equation and simply manipulate each part into its equivalent until the other side of the equation was...

As a consequence of Bezout's identity, if a and b are coprime there exist integers x and y such that: ax + by = 1 The extension states that, if a and b are coprime the least natural number k for which all natural numbers greater than k can be expressed in the form: ax + by Is a+b-1...

Homework Statement I am trying to prove that \displaystyle{\not} a \displaystyle{\not} b + \displaystyle{\not} b \displaystyle{\not} a = 2a\cdot b using the relation \{\gamma^{\mu},\gamma^{\nu}\} = 2g^{\mu\nu} Homework Equations The Attempt at a Solution If I work backwards...

I have been working on this for a few days and cannot prove this: [SIZE="5"]J[SIZE="2"]-3/2 [SIZE="5"](x)=\sqrt{\frac{2}{\pi x}}[SIZE="6"][\frac{-cos(x)}{x} [SIZE="5"]- [SIZE="4"]sin(x) [SIZE="6"]] Main reason is \Gamma[SIZE="4"](n-3/2+1) give a negative value for n=0 and possitive value...

Homework Statement Given that n independent tosses having probability of p of coming up heads are made, show that an even number of heads results is 0.5(1+(q-p)^n) where q is 1-p, by proving the identity Sigma from i=0 to n/2 of (n choose 2i) (p^2i)(q^(n-2i))=0.5(((p+q)^n)+(q-p)^n)...

Homework Statement (1 + cosθ) / (1 - cosθ) = (1 + secθ) / (secθ - 1) Homework Equations using only the quotient identities, pythagorean identities, and reciprocal identities The Attempt at a Solution didnt know where to start...

I am trying to prove the identity S_{12} ^ 2 = 4S^2-2S_{12} where S12 is the tensor operator: S_{12} = 3(\vec{\sigma_1} \vec{r})(\vec{\sigma_2} \vec{r}) / r^2 - (\vec{\sigma_1} \vec{\sigma_2}) where sigmas are vectors made of the Pauli matrices in the space of particle 1 and 2, and \vec{S}...

Homework Statement Given f[f(x)] = 2x + 1 find all linear functions that satisfy this identity. Given f[f[f(x)]] = 2x + 1 find all linear functions that satisfy this identity. 2. The attempt at a solution I have not started to attempt a solution at this because I have no idea how to...

Homework Statement Okay so the objective here is to express y(t) = cos(t - b) - cos(t) in the form y(t) = Asin(t - c) where A and c are in terms of b.Homework Equations For easy reference, here is a table of identities: http://www.sosmath.com/trig/Trig5/trig5/trig5.html The Attempt at a...

I'm trying to show that: F(a, b; z) = F(a-1, b; z) + (z/b) F(a, b+1 ; z) where F(a, b; z) is Kummer's confluent hypergeometric function and F(a, b; z) = SUM[SIZE="1"]n=0[ (a)[SIZE="1"]n * z^n ] / [ (b)[SIZE="1"]n * n!] where (a)[SIZE="1"]n is the Pochhammer symbol and is...

Homework Statement By appropriate limiting procedures prove the following expansion: J_0 (k\sqrt {\rho ^2 + \rho '^2 - 2\rho \rho '\cos (\phi )} ) = \sum\limits_{m = - \infty }^\infty {e^{im\phi } J_m (k\rho )J_m (k\rho ')} Homework Equations...

1. This was actually a center of mass problem, so I got the equation below: 2.[T_2*sin(theta2)] / [T_1*sin(theta1) + T_2*sin(theta2)][b] [b]3. This is part of a solution I obtained for a physics problem. I know there is some trick with a trig indentity that I can use to simplify...

I've encountered an equation in my textbook where a formula for t is given: t = \frac{2}{3H_0 \Omega_{\lambda}^{1/2}} \ln \left( \frac{1 + \cos \theta}{\sin \theta} \right ) where, \tan \theta = \left( \frac{\Omega_0}{\Omega_{\lambda}}\right)^{1/2} (1 + z)^{3/2} So, basically, t is...

[b]1. Verify this identity: a*sin Bx + b*cos Bx = sqrt(a^2 + b^2)sin(Bx + C) where C= arctan b/a [b]2. a/sqrt(a^2+b^2)sin Bx + b/sqrt(a^2+b^2)cos Bx=cos C sin Bx + sin C cos Bx= [b]3.a*sin Bx + b cos Bx = sqrt(a^2 + b^2) sin(Bx + C) Homework Statement Homework Equations...

I read the following expression in a book: \int_{-\infty}^{\infty} \dfrac{1}{t(1-t)} \log \left| \dfrac{t^{2} q^{2}}{(p-tq)^{2}} \right| ~ dt = - \pi^{2} p and q are both timelike four-vectors, so p², q² > 0 This integral was solved by using the identity \lim_{s \to \infty}...

Homework Statement (sin 3α/sin α) - (cos 3α/cosα) =2 Homework Equations The Attempt at a Solution I know for sin 2 α I would put 2 sinαcosα, so for 3α, do I just put 3sinαcosα? for cos 3α, I'm sort of clueless because there's 3 we can use for cosine, Then after that step, I...

Homework Statement cos(α − β)cos(α + β) = cos2α - sin2 β Homework Equations cos(α + β) = cos α cos β − sin α sin β cos(α − β) = cos α cos β + sin α sin β The Attempt at a Solution I worked out the LHS which makes it cos2α cos2β - sin2α sin2β=RHS Then, I'm stuck, however, i...

If f(x,y,z) = xi + yj +zk, prove that Jacobian matrix Df(x,y,z) is the identity matrix of order 3. Because the D operator is linear, D1f(x,y,z) = i, D2f(x,y,z) = k, D3f(x,y,z) = k There is clearly a relationship between this and some sort of identity, but I'm not sure how to state it, and...

Homework Statement Could someone please tell me how to expand: ∆ x [(u.∆)u] Homework Equations [b]3. The Attempt at a Solution thankyou

e^{i\pi}=-1 e^{i\frac{\pi}{2}}=i but e^{i\frac{\pi}{3}}\neq-1 I know there are infinitely many solutions here, but I would expect the third result should include -1 as the cube root of itself. However e^{\pm ix}=cos(x)\pm{isin(x)} would not seem to give -1 for any solution for...

I'm looking over the differential equation describing a hanging cable in a textbook, and I probably need to review my trigonometric derivatives and integrals again because I'm not seeing how they got the following: \frac{dy}{dx} = tan(\phi) \frac{ws}{T_0} \frac{d^2y}{dx^2} =...

Homework Statement I have $\int \nabla^2 \vec{u} \cdot \vec{v} dV$ where u and v are velocities integrated over a volume. I want to perform integration by parts so that the derivative orders are the same. This is the Galerkin method. Homework Equations The Attempt at a Solution I have...

Homework Statement lim t3/tan32t t->0 The Attempt at a Solution I am stuck I have a lot of trouble with trig identities

Homework Statement Simplify this expression: f(t) = sin(\betat)*cos(\betat) Homework Equations Identities The Attempt at a Solution I started out by doing sin(\betat)*sin(\betat+\pi/2) but I can't go anywhere from there. If I use the sin(a+b) formula it brings me back to the original...

Hello everyone. I officially have the worst Trig teacher in America and I have never been so confused in a math class before. I have at least 5 problems (only 2 posted here) I'm struggling with and need to figure out before my exam tomorrow. Any help is much appreciated. 1. Homework Statement...

Homework Statement Let f(x,y,z) be a function of three variables and G(x,y,z) be a vector field defined in 3D space. Prove the identity: div(fG)= f*div(G)+G*grad(f) Homework Equations For F=Pi +Qj+Rk div(F)=dF/dx + dQ/dy + dR/dz grad(F)=dF/dx i + dQ/dy j + dR/dz k The...