Identity Definition and 1000 Threads

Homework Statement prove that (sinA +sin3A + sin5A)/(cosA + cos3A + cos5A) = tan3A Homework Equations sinP + sinQ = 2sin((P+Q)/2)cos((P-Q)/2) cosP + cosQ = 2cos((P+Q)/2)cos((P-Q)/2) The Attempt at a Solution (sin3A + sinA) + sin5A = 2sin2AcosA + 2sin((5/2)A)cos((5/2)A) (cos3A +...

Hi guys! When I'm doing math problems with multiples variables and I have to build up equations, I often come up with identities rather than the variable equal to a value. Is there anyway to understand how we have to build up the equations without obtaining an identity at the end? Thank you.

Hi all; Look at the attached part from Van Dalen's Logic and structure. What is he doing exactly? In axiomatizing 'Identity' as he does, what is gained rather than what we had before (i.e., looking at 'Identity' as a binary predicate)?! Even in the axioms, he is again using a symbol in the...

I guess the best way to start this is by admitting that my conceptual understanding of the Cauchy-Schwarz Inequality and the Lagrange Identity, as the title suggests, is not as deep as it could be. I'm working through Marsden's 3e "Basic Complex Analysis" and it contains a proof of the Cauchy...

I am reading Mohapatra's book: "Massive Neutrinos in Physics and Astrophysics". At the beginning of chapter 7, it is sought expressions where the right neutrino was considered in the Electroweak Standard Model. Everything was fine until I found the expression...

I was reading a paper by Geroch and I was confused by the following: given a scalar field ##\omega## satisfying ##\nabla_{a}\omega = \omega_{a} = \epsilon_{abcd}\xi^{b}\nabla^{c}\xi^{d}## and the scalar ##\lambda = \xi^{a}\xi_{a}##, where ##\xi^{a}## is a killing vector field, can someone prove...

I am trying to resolve a trig identity for some notes I am typing up. On paper, I wrote recall $e(\sin(E_1) - \sin(E_0)) = 2\cos(\zeta)\sin(E_m)$. I have no idea what I am recalling this from now at least. Identities I have set up are: \begin{align} E_p &= \frac{1}{2}(E_1 + E_2)\\ E_m &=...

Homework Statement Let a and b be integers and m an integer >1 Evaluate [b/m] + [(b+a)/m]+ [(b+2a)/m]+ [(b+3a)/m]+ [(b+4a)/m]+ [(b+5a)/m]+...+ [(b+(m-1)a)/m] Homework Equations The Attempt at a Solution i tried to use hermite identity. [x] + [x + 1/n] + [x + 2/n] +...+ [x +...

Homework Statement Use the Jacobi identity in the form $$ \left[e_i, \left[e_j,e_k\right]\right] + \left[e_j, \left[e_k,e_i\right]\right] + \left[e_k, \left[e_i,e_j\right]\right] $$ and ## \left[e_i,e_j\right] = c^k_{ij}e_k ## to show that the structure constants ## c^k_{ij} ## satisfy the...

Prove $$\frac{\sin\left(5\tfrac{3}{4}^{\circ} \right)}{\cos\left(17\tfrac{1}{4}^{\circ} \right)}+\frac{\sin\left(17\tfrac{1}{4}^{\circ} \right)}{\cos\left(51\tfrac{3}{4}^{\circ} \right)}+\frac{\sin\left(51\tfrac{3}{4}^{\circ} \right)}{\cos\left(155\tfrac{1}{4}^{\circ}...

It is often stated that this is the case, but I have often wondered if it is a general statement or just something that we observe to be the case when calculating the relevant loop corrections. Can it be proven generally? Is it somehow easy to see?

In Peskin at page 248 he finds that if he calculates the vacuum polarization that $$\Pi(q)^{\mu \nu} \propto g^{\mu \nu}\Lambda^2$$ a result which violates the Ward identity and would cause a non-zero photon mass $$M \propto \Lambda$$. But as Peskin states, the proof of the Ward identity...

Hey guys,I need some help on the following trig identities: 1) sin2x = 2tanx/1+tan^2x 2) sin2x/sinx - cos2x/cosx = secx My attempts: 1) LS: sin2x 2sinxcosx 2sinx/cosx 2tanx/1+tanx Not sure if this is right or not. I kind of understand my third step but it just doesn't seem...

Homework Statement Calculate the following integral: \int_{0}^{2\pi}(\sum_{k=0}^{\infty} \frac{\cos(kx)}{3^k})^2 dx Homework Equations Parseval's identity: \frac{1}{2 \pi} \int_{-\pi}^{\pi} {|f(x)|^2 dx} = \sum_{n=0}^{\infty} {|a_n|^2+|b_n|^2} Where a_n, and b_n are the trigonometric...

Homework Statement I want to compute the electric field knowing the magnetic field using a vector identity Homework Equations E=i \frac{c}{k} (∇\timesB) B(r,t)=(μ0ωk/4π) (\hat{r}×\vec{p})[1-\frac{1}{ikr}](eikr/r) \vec{p}=dipole moment,constant vector we have ti use the identity...

The Ward-Takahashi identity for the simplest QED vertex function states that $$q_\mu \Gamma^\mu (p + q, p) = S^{-1}(p+q) - S^(p)^{-1}.$$ Often the 'Ward-identity' is stated as, if one have a physical process involving an external photon with the amplitude $$M = \epsilon_\mu M^\mu$$...

Hello MHB. How can i proof this equation? log(x).log(x^2).log(x^3)... log(x^90)=4095

Hello. Please tell me how do I derive: cos(θ)=1/2 (e^{iθ}+e^{-iθ}) from: e^{iθ}=cos(θ) + isin(θ) as well as: sin(θ)=1/2i (e^{iθ}-e^{-iθ}) I can't figure it out...for example, where does the 1/2 come from? Thank you:smile:

Hello there, I have a problem I'm hoping someone can help me with. I'm writing a bit of code for computing the value of pi that converges faster than a previous piece that relies on the leibniz series. Anyway, I'm struggling with showing how this identity arises. tan(2t) = 2 * tan(t) / 1 -...

Let A be the set of n \times n matrices. Then the identity element of this set under matrix multiplication is the identity matrix and it is unique. The proof follows from the monoidal properties of multiplication of square matrices. But if the matrix is not square, the left and right...

Here is the question: Here is a link to the question: Help with precalculus! Sum or difference formula? - Yahoo! Answers I have posted a link there to this question so the OP can find my response.

I have this equation 1/(r^2+l^2)^(3/2) and I need to integrate it quickly. My first thought is using this integral formula 1/(1+x^2)^(3/2)=x/sqrt(1+x^2) but how exactly do I get my equation into that form?

Hi all, I found this "identity" online on Wikipedia, and realized that it would actually come in pretty useful for me, if only I could prove that it is true. Can you guys help me on that?: $$\sum_{k=1}^nk^m=\frac{1}{m+1}\sum_{k=0}^{m}\binom{m+1}{k}B_k\;n^{m-k+1}$$ where ##B_k## denotes the kth...

1. Prove:\frac{cscx +cotx}{cscx-cotx} = \frac{1+2cosx+cos^2x}{sin^2x} Homework Equations tanx = \frac{sinx}{cosx} cotx = \frac{cosx}{sinx} cscx secx cotx sin^2x + cos^2x = 1 The Attempt at a Solution Left side: =\frac{cscx +cotx}{cscx-cotx} =\frac{1/sinx + cosx / sinx}{1/sinx - cosx/sinx}...

So I'm trying to get through euler's introduction to the analysis of the infinite so I could eventually read his books on calculus but I'm stuck somewhere and can't seem to figure out how he equates this identity so by expanding I get sin(2y) * cos(z) + cos(2y) * sin(z). I get that the...

Over the years, I am slowly becoming more radicalized about what QM is trying to tell us about our world. I am coming to a point where I am close to giving up entirely by just saying that it tells us nothing at all (don't get too bothered by this statement... just let me explain...). We are...

Homework Statement \widetilde{F}(r)=F1(r)i+F2(r)j+F3(r)k \hat{r}=r/r r(x,y,z)=xi+yj+zk, r=abs(r)=sqrt(x2+y2+z2) (Hint: The chain rule will be helpful for this question.) Show that: \nabla\cdotF = \hat{r}\cdotdF/dr. Homework Equations The Attempt at a Solution My attempt...

"Sum to Product" Trigonometric identity does not work Hi, The identity [SIZE="3"]sin(u) + sin(v) = 2 * sin (\frac{u+v}{2}) * cos(\frac{u-v}{2}) http://en.wikipedia.org/wiki/List_of_trigonometric_identities#Product-to-sum_and_sum-to-product_identities Does not always work. I put the equation...

Jacobi identity in local coordinates?!? Apparently (i.e. according to an article written by physicists), the Jacobi identity for the Poisson bracket associated to a Poisson bivector \pi = \sum\pi^{ij}\partial_i\wedge\partial_j is equivalent to...

Homework Statement Consider a stationary solution with stress-energy ##T_{ab}## in the context of linearized gravity. Choose a global inertial coordinate system for the flat metric ##\eta_{ab}## so that the "time direction" ##(\frac{\partial }{\partial t})^{a}## of this coordinate system agrees...

Homework Statement Homework Equations ImA = AIn = A. (A−1)−1 = A (AB)−1 = B−1A−1 The Attempt at a Solution Determinates: Det(A) = 3 – 0 = 3 Det (2A+BT) = 4 – 8 = -2 Matrices B^T = 2 -2 0 -5 (2A + B^T)^-1 = -8 -4 -8 -2 So I've kinda figured...

Here is the question: Here is a link to the question: Prove the identity, pre calc!? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Hi, I have been trying to solve this difficult problem for some time and I thought of at least two ways to prove it but to no avail...the second method that I thought of was to employ binomial expansion on the denominator and that did lead me to the result where it only has x terms in my final...

I'm trying to rotate a point about the origin (0,0,0) and starting with an identity matrix, this works fine for the x- and y-rotation axes, but fails with the z-axis, where the point just sits in place. \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} M_{ID} \times M_Z...

Homework Statement Find and prove the identity sec^-1(x) in terms of cos^-1(arg) (Note that 1/cos^-1(x) is not equal to sec^-1(x). Homework Equations None. The Attempt at a Solution sec(sec^-1(x)) = x 1/cos(sec^-1(x)) = x 1/cos(cos^-1(x)) = 1/x 1/cos(cos^-1(1/x)) = 1/1/x...

Homework Statement Prove the identity: $$\csc(2\theta)-\cot(2\theta)\equiv\tan(\theta)$$ Homework Equations The Attempt at a Solution Starting with the LHS: $$\csc(2\theta)-\cot(2\theta)$$ $$\frac{1}{\sin(2\theta)}-\frac{\cos(2\theta)}{\sin(2\theta)}$$...

Homework Statement Using the operator identity: \hat{L}^2=\hat{L}_-\hat{L}_+ +\hat{L}_z^2 + \hbar\hat{L}_z show explicitly: \hat{L}^2 = -\hbar^2 \left[ \frac{1}{\sin^2\theta} \frac{\partial^2}{\partial\phi^2} + \frac{1}{\sin\theta} \frac{\partial}{\partial\theta}...

Homework Statement Given the following two triangles: Show that v \cos{\delta} = V(1-\cos{\beta})+u\cos(\alpha - \beta) The Attempt at a Solution Using the cosine law I've got: v^{2}=x^{2}+V^{2}-2xV\cos{(\theta + \beta)} and u^{2}=x^{2}+V^{2}-2xV\cos{(\theta)} I figured maybe using the...

Hi all, I found this rather interesting formula online and I was wondering what it means. Could someone explain it to me? All help is appreciated: http://functions.wolfram.com/IntegerFunctions/Floor/16/03/0001/

Homework Statement a^{log_{b}(c)}=c^{log_{b}(a)} The Attempt at a Solution Take log_{a} of both sides: log_{a}(a^{log_{b}(c)})=log_{a}(c^{log_{b}(a)}) gives: log_{b}c=log_{b}alog_{a}c Looks like one more step for the RHS. I sort of see that the RHS should become log_{b}c and...

On page 273 of Dummit and Foote the last sentence reads: (see attachment - page 273) "The notion of the greatest common divisor of two elements (if it exists) can be made precise in general rings." (my emphasis) Then, the first sentence on page 274 reads as follows: (see attachment - page...

(Hungerford exercise 31, page 143) Let R be a commutative ring without identity and let a \in R Show that A = \{ ra + na \ | \ r \in R, n \in \mathbb{Z} \} is an ideal containing a and that every ideal containing a also contains A. (A is called the prinicipal ideal generated by a)

Homework Statement (question attached) Homework Equations The Attempt at a Solution Checking solution.. pretty sure I did this wrong. (solution attached)

Homework Statement Use ##D = \frac{d}{dx}##as a differential operator and the following $$(D - a)(D -b)[f(x)e^{\lambda x}] = e^{\lambda x} (D + \lambda -a)(D + \lambda -b)f(x)$$ to obtain $$(D^2 + D +1)[(Ax^2 + Bx + C)e^{ix}] = (iAx^2 + [iB + (4i + 2)A]x + 2A + (2i + 1)B + iC)e^{ix}$$ The...

Homework Statement Hello PF! This is not a homework problem but I am curious to know if the following combinatorial identity exist: \sum^{r-1}_{k=0} (^{n-1}_{r-(k+1)}) \times (^{r}_{k}) = (^{n+r-1}_{r-1}) Much thanks :)

I just need to know how can Mathematica recognize e^{-i\theta} as the eulers identity. This is, e^{-i\theta} = cos \theta + sin \theta . When i plot a function like e^{i\theta}, nothings appear in the graph. Help is appreciated.

Homework Statement prove, ∇x(ψv)=ψ(∇xv)-vx(∇ψ) using levi civita symbol and tensor notations Homework Equations εijkεimn=δjnδkm-δknδjm The Attempt at a Solution i tried for nth component εnjk (d/dxj)εklm ψl vm εknjεklm (d/dxj) ψl vm using εijkεimn=δjnδkm-δknδjm...

Dear all, Any idea for the proof of the Lagrange's identity using tensor notations and Levi Civita symbol? (a x b).(c x d)=(a.c)(b.d) - (a.d)(b.c) x: cross product a,b,c,d: vectors Thanks

Homework Statement Let R be a ring with identity, and a,b are elements in R. If ab is a unit, and neither a nor b is a zero divisor, prove a and b are units. Homework Equations If ab is a unit then (ab)c=1=c(ab) for some c in R. The Attempt at a Solution Assume both a and b are...

cosθ + sinθ = √2 cos(θ-∏/4) what are the steps in between?