Identity Definition and 1000 Threads

Homework Statement Hi guys, How can sin(∏)cos(ω∏)-cos(∏)sin(ω∏) = sin(ω∏)? please guide me trigonometry identity to apply with this? Homework Equations The Attempt at a Solution

Show that cosh(x) = 1 => x = 0 I am only allowed to use the definition of cosh, the algebraic rules for the exponential function, that exp(x2)>exp(x1) for x2 > x1, and the fact that we have defined it with the requirement: exp(x) ≥ 1 + x The exp(x) term of course is not trouble. What...

Here is the question: Here is a link to the question: http://answers.yahoo.com/question/index?qid=20130130130636AAOqgvz I have posted a link there so the OP can find my response.

Gradient of a dot product identity proof? Homework Statement I have been given a E&M homework assignment to prove all the vector identities in the front cover of Griffith's E&M textbook. I have trouble proving: (1) ∇(A\bulletB) = A×(∇×B)+B×(∇×A)+(A\bullet∇)B+(B\bullet∇)A Homework...

If you're just given x2+y2=1, how would you know if it's an equation or an identity? Functions are identities, right?

Item on bill from lawyer: Crossed street to talk to you; it wasn't you: .$30.00 Fred was riding with his lawyer friend Jack. "Jack, you're a good guy, but you lawyers think of nothing but money." "That's not true," said Jack. "I'm only seeking justice for my clients." Just then a truck roared...

Hey guys~ I was looking for a way to derive a formula for fn (the nth term in the fibonacci sequence). While looking for this, I came across a potential solution using the residue theorem. Using the generating function Ʃk≥0 fnzn, find the identity for fn. The problem looks like the right...

Homework Statement cos(x)^2/(1+3sin(x)-4sin(x)^2)=(1+sin(x))/(1+4sin(x))Homework Equations We are taking a topic in math where you rearrange one side of the formula to match the otherThe Attempt at a Solution I have factor 1+3sin(x)-4sin(x)^2 to get (-sin(x)+1)(4sin(x)+1)

Homework Statement If sin^{-1}x+sin^{-1}y+sin^{-1}z = \pi then prove that x\sqrt{1-x^2}+y\sqrt{1-y^2}+z\sqrt{1-z^2}=2xyz Homework Equations The Attempt at a Solution I assume the inverse functions to be θ, α, β respectively. Rearranging and taking tan of both sides tan(\theta +...

Homework Statement Prove that : \frac{cos(x)-1}{(1-cos(x))^{3}} = -\frac{1}{4sin^{4}(0.5x)}Homework Equations None that I can think of. Maybe the double angle formula... The Attempt at a Solution I couldn't do much in this question : -\frac{1}{(1-cos(x))^{2}}

Let $G$ be a finite group, $T$ an automorphism of $G$ with the property that $T(x)=x$ if and only if $x=e$. Suppose further that $T^2=I$, that is, $T(T(x))=x$ for all $x\in G$. Show that $G$ is abelian. I approached this problem using the permutation representation afforded by $T$ on $G$. Its...

Homework Statement Show e^{\frac{x}{2}(t-\frac{1}{t})}=\sum^{\infty}_{n=-\infty}J_n(x)t^n Homework Equations J_k(x)=\sum^{\infty}_{n=0}\frac{(-1)^n}{(n+k)!n!}(\frac{x}{2})^{2n+k} The Attempt at a Solution Power series product (\sum^{\infty}_{n=0}a_n)\cdot (\sum^{\infty}_{n=0}...

Well a common question arises out of my mind that Local IP addresses assigned by ISP are stored...that's ok...But happens when I connect myself to a Proxy server...My identity is protected..isn't it...So even if I do something wrong I won't be prosecuted as because the convict is the proxy...

Homework Statement Simplify (2cos2x-cos4x)/(2cos2x+cos4x) The Attempt at a Solution I let θ = 2x (2cosθ-cos2θ)/2cosθ+cos2θ) Since cos2θ= 1-2cos^2 (2cosθ-(1-2cos^2)/2cosθ+1-2cos^2 But I get lost when applying it and can't get beyond this, Do i have to use the quadratic...

Homework Statement Need some help finding all solutions for x... csc^2((x)/(2)) = 2secx The Attempt at a Solution Not sure what kind of approach to take but: 1/ sin^2(x/2) = 2/ cos x From here Not sure what to do i tried cross multiplying and got cos x = 2sin^2(x/2) but got...

I was wondering about this: The identity operator writes a vector in the basis that is used to express the identity operator: 1 = Ʃlei><eil But if you are to apply it to a vector in a given basis A should the lei> then be expressed in terms of their own basis or in terms of A?

In the notes it says that \text{v}\cdot \nabla \text{u} = |\text{v}|\frac{du}{dl} \text{v} = (a(x,y), b(x,y)) l is the arclength in the v-direction. Why is this? The LHS is the projection of v onto the gradient of u, the other thing is the magnitude of v, multiplied by the du/dl.

This isn't a homework help issue, I just want to know what identity(?) this is. a/b to ab or A^2/B^2 to (A^2)(B^2)

Hi all, I have a question that seems very simple but I just do not see it;) Let α denote an r×1 vector with arbitrary entries; I'm trying to construct an 1×r vector m such that αm = I, where I is the r×r identity matrix... The first question is: is this possible? I tried the...

I am curious about under what conditions the powers of a square matrix can equal the identity matrix. Suppose that A is a square matrix so that A^{2} = I At first I conjectured that A is also an identity matrix, but I found a counterexample to this. I noticed that the counterexample...

I am trying to integrate -tan(x)sec^2(x) and getting -tan^2(x) / 2. When I put it in wolfram alpha it gets the same answer when I press show solution, but without pressing it it shows -sec(x)/2. So I am wondering, is it the case tan^2(x) = sec(x)?? I don't remember this as a correct trig...

Homework Statement e_j=g_(jk)e^k where e_j is a covariant vector base e^k is a a contravariant vector base g_(jk) is the covariant metric Homework Equations The Attempt at a Solution

How should one prove that the integers form a commutative ring? I am not sure exactly where to go with this and how much should be explicitly shown. A ring is meant to be a system that shares properties of Z and Zn. A commutative ring is a ring, with the commutative multiplication property...

Homework Statement Prove the Identity sinθ/(1+cosθ) = 1-cos(θ)/sinθ Homework Equations sinθ/cosθ = tanθ sin^2θ + cos^2θ = 1 The Attempt at a Solution sinθ/(1 + cosθ) = LS cosθtanθ/(1+cosθ) = LS cosθtanθ/(sin^2θ + cos^2θ + cosθ) = LS cosθtanθ/(tan^2θcos^2θ +...

Let B_{k}(x)=\sum_{n\geq 0}\binom{n}{k}\frac{x^{n}}{n!}. Show that B_{k}(x)B_{l}(x)=\frac{1}{2^{k+l}}\binom{k+l}{l}B_{k+l}(2x). I'm having some trouble with this one. Does anyone have any hints? I've tried using Cauchy product and Chu-Vandermonde equality but I get...

Suppose T belongs to L(V,V) where L(A,W) denotes the set of linear mappings from Vector spaces A to W, is such that every subspace of V with dimension dim V - 1 is invariant under T. Prove that T is a scalar multiple of the identity operator. My attempt : Let U be one of the sub spaces of V...

Prove that ∇.(u×v) = v.(∇×u) - u.(∇×v), where "." means dot product and u,v are vectors. So by scalar product rule, A.(B×C) = C.(A×B) So applying same logic to above identity, shouldn't the left hand side just be equal to v.(∇×u)? Or just to -u.(∇×v), since A.(B×C) = -B.(A×C) ?

assuming that the system (s,*) has an identity element. if the equation (a*b)*(c*d)=(a*c)*(b*d) holds for all a,b,c,d belongs to S , ,prove that:* is associative and commutative . I tried so much but with no good result ! any ideas ?

Prove the Identity by Using a Sign Reversing Involution (See Attachment)

(sin^3(x)-cos^3(x))/(sinx-cosx) = 1+(sinx*cosx) I'm following a path similar to the post on http://www.askmehelpdesk.com/mathematics/verify-identity-sin-3-x-cos-3-x-sin-x-cos-x-1-sin-x-cos-x-500483.html However, I keep getting 1-(sinx*cosx) when solving for mine as I end up with...

Hi, I cannot find any other reference to this formula: sin(x)/cos(x-1) it seems to fit with Euler's identity as given by Wikipedia. Euler's identity is a special case of this identity equation. I've actually posted this on the Wikipedia page to see if I can get confirmation of this or...

Homework Statement Homework Equations Any trig formulas The Attempt at a Solution The yellow paper is me switching everything to sin and cos to see if that helps but it doesn't. I'm completely stuck here.

I'm having trouble understanding a trig identity and only include it here (rather than in trig forum) as it touches on a -broader- derivative problem. Here it is: $$\frac{d}{dx} \ e^{sin^2(x)}=e^{sin^2(x)}\cdot 2sin(x)cos(x)$$ $$=e^{sin^2(x)}\cdot \ sin(2x)$$ I have attached a proof of the...

Homework Statement Prove that: ∇×(a∙∇a) = a∙∇(∇×a) + (∇∙a)(∇×a) - (∇×a)∙∇a Homework Equations Related to the vorticity transport equation. The Attempt at a Solution Brand new to index/tensor notation, any suggestions on where to begin? For example, I am having trouble...

proving the "contracted epsilon" identity in the wikipedia page for the Levi Civita symbol, they have a definition of the product of 2 permutation symbols as: ε_{ijk}ε_{lmn} = δ_{il}(δ_{jm}δ_{kn} - δ_{jn}δ_{km}) - δ_{im}(δ_{jl}δ_{kn} - δ_{jn}δ_{kl}) + δ_{in}(δ_{jl}δ_{km} - δ_{jm}δ_{kl}) and...

Hello! I should prove: \delta'(\lambda x) = \dfrac{1}{\lambda \vert \lambda \vert} \delta(x), where lambda is just a constant. If we make use of the scaling property and the definition of the distributional derivative, we find: \left( \delta'(\lambda x), f \right) =...

Homework Statement Prove the following vector identity: Any vector a dotted with its time derivative is equal to the vector's scalar magnitude times the vector's derivative's scalar magnitude. Homework Equations (a)dot(d(a)/dt)=||a|| x ||da/dt|| The Attempt at a Solution I...

Homework Statement I need to prove the identity: (a×b)\cdot(c×d)= (a\cdotc)(b\cdotd)-(a\cdotd)(b\cdotc) using the properties of the vector and triple products: Homework Equations a×(b×c)=b(a\cdotc)-c(a\cdotb) a\cdot(b×c)=c\cdot(a×b)=b\cdot(c×a) The Attempt at a Solution I...

Hi there, working on a physical problem I found two functions that should be equivalent, and indeed they seem to be after a numerical check. The functions are shown in the attached PDF. I can not figure a way to prove their equivalence analytically (the double integral especially gives me...

Can anyone help me in proving the following identity: (\gamma ^{\mu} )^T = \gamma ^0 \gamma ^{\mu} \gamma ^0 I understand that one can proceed by proving it say in standard representation and then proving that it's invariant under unitary transformations. this last thing is the one...

Hey guys, this is for my classical E&M class but it's more of a math problem. Homework Statement Show: ∇(\vec{A} . \vec{B}) = \vec{B} \times (∇ \times \vec{A}) + (\vec{B} \times ∇)\vec{A} + \vec{A} \times (∇ \times \vec{B}) + (\vec{A} \times ∇)\vec{B} Homework Equations I tried...

Hello everybody. Here's the problem: $$\text{Let } R \text{ be a ring with identity. Let }a \in R \text{ and suppose that exists an unique } a' \in R \text{ such that }a a' =1. \text{ Prove that } a'a=1.$$ My solution: Since we have an identity, it has an inverse (itself), which means we can...

Homework Statement If G is a group, a is in G, and a*b=b for some b in G (* is a certain operation), prove that a is the identity element of G Homework Equations The Attempt at a Solution I feel like you should assume a is not the identity element and eventually show that a= the...

Hello everyone, I came across this identity while browsing Wikipedia, and I decided to try to prove it for myself. ( It was discovered by S Ramanujan) \int_0^\infty \cfrac{1+{x}^2/({b+1})^2}{1+{x}^2/({a})^2} \times\cfrac{1+{x}^2/({b+2})^2}{1+{x}^2/({a+1})^2}\times\cdots\;\;dx =...

It seems that this term comes up in solving the cubic equation. While there is the identity for the half-angle, there doesn't seem to be one for third-angle.

Homework Statement I do not understand equal signs 2 and 3 the following Angular momentum operator identity: Homework Equations \hat{J}^2 = \hat{J}_1^2+\hat{J}_2^2 +\hat{J}_3^2 = \left(\hat{J}_1 +i\hat{J}_2 \right)\left(\hat{J}_1 -i\hat{J}_2 \right) +\hat{J}_3^2 + i...

Homework Statement Simplify the following: (1/cos2θ) - (1/cot2θ)Homework Equations Various trig identities The Attempt at a Solution I tried to make cos2θ into 1-sin2θ and cot2θ into csc2θ-1 but still couldn't find any obvious solution. Help?

Show that: 4(\sin^4x+\cos^4x) \equiv \cos4x + 3. Really stuck with this, no idea how to go ahead with it. The book gives a hint: \sin ^4 x = (\sin ^2 x)^2 and use \cos 2x = 1 - 2\sin ^2 x But I don't even understand the hint, where did they get \cos 2x = 1 - 2\sin ^2 x from?

Prove: \frac{CosθSinθ}{1 + Tanθ} = Cos2θ =========================== I multiply out the denominator to get: CosθSinθ = Cos2θ + CosθSinθ I cannot seem to prove it. Starting to think it's a trick question.. :/