Identity Definition and 1000 Threads

Homework Statement cos^2x-cotx --------------- = cot^2x sin^2x-tanx Homework Equations The Attempt at a Solution every solution I get gives me a zero, not cot^2

Is it true that if \sigma \in S_n is a cycle of length k \leq n, then \sigma^k = \varepsilon, where \varepsilon is the identity permutation, and that k is the least nonzero integer having this property?

Homework Statement I'm finally starting to understand proving trig identities, but I have just one more that I can't seem to figure out. secx - tanxsinx = cosx Homework Equations N/A The Attempt at a Solution Well first, I multiplied the tanx and sinx and came up with sin2x /...

0.15348=0.1415cosβ -0.291sinβcosβ how do i solve this equation with both sinβ and cosβ, i realize that i need to play with the identities but have had no luck, please help i tried squaring the whole thing, and saying cos2β=t, then i get 0.023556=0.02t - 0.582\sqrt{t-1}\sqrt{t}...

Prove this using this identity: k\binom{n}{k}=n\binom{n-1}{k-1} \binom{n}{1}-2\binom{n}{2}+3\binom{n}{3}+...+(-1)n-1\binom{n}{n} I was able to do this via differentiation, but not using this substitution. Any hints would be great.

\sumk=0n\binom{n}{k}2=\binom{2n}{n} Could someone give me a hint as to how to start this. I'm not sure how to really interpret it. (n-k)\binom{n}{k}=n\binom{n-1}{k} Right Side: Suppose you create a committe from \binom{n}{k} , then to pick a leader who isn't in the committee but...

Homework Statement (1-cosx)/(1+cosx) = (cscx-cotx)^2 Homework Equations cscx = 1/sinx, cotx = cosx/sinx, sin^2x + cos^2x = 1 The Attempt at a Solution I have tried many different attempts, but I can't seem to make one side like the other. I took the (cscx-cotx)^2 and expanded it...

Homework Statement solve 3cos(x) + 3 = 2 sin^2(x) where 0 <= x < 2piHomework Equations The Attempt at a Solution 3(cos(x) + 1) = 2 sin^2(x) 3(cos(x) + 1) = 2 (1- cos^2(x)) I've tried this variation, and a couple others but it just does not pan out. Please help. Oh yeah we have a real...

\sum_{m=k}^{n-k}\binom{m}{k}\binom{n-m}{k}=\binom{n+1}{2k+1} I'm not sure how to prove it, I understand the combinatorial proof..i.e. putting it to an example...but i can't derive one side and get the other.

i do not remember the webpage i watched this but i remember that they said ' IN chapter 1 of his notebook Ramanujan wrote ' \sum_{n=0}^{x}n^{r}= (r+1)^{-1}x^{r+1}+ \zeta (-r) - \sum_{k}B_{2k}\frac{\Gamma (r+1)}{\Gamma (k-2r+2)} does anyone knows how to get this ??

Help please on trig identity Homework Statement Simplify cot2xsecx + 1/cosx The Attempt at a Solution Well so far i got: cot2xsecx + 1/cosx =(cos2x/sin2x)(1/cosx) + 1/cosx =((1+cos2x)/(1-cos2x))(1/cosx) + 1/cosx and from there I am stuck, I've tried playing around with it...

Homework Statement Prove Lagrange's identity for real numbers http://mathworld.wolfram.com/LagrangesIdentity.html The Attempt at a Solution I tried one of the methods used in proving the Cauchy-Schwarz inequality (Ax^2 + Bx + C is greater than or equal to zero, where a = the sum from...

There are two things about this identity that I don't understand: 1. Why is it equivalent to a statement of charge conservation? 2. Wikipedia claims that it is like a quantum version of the classical noether's theorem. In what sense is this true? Thanks

Homework Statement Must be proven algebraically, duh! Homework Equations trig identities The Attempt at a Solution I'm at a loss as what to do next. Any help would be appreciated.

Homework Statement I'm trying to find what a a left and right identity element is. Also, I want to see if a one sided element for * exists, if it is unique. Homework Equations The Attempt at a Solution Ok, I just don't really know what a one sided element is. I'm using...

Let X and X' denote a single set in the two topologies T and T', respectively. Let i:X'-> X be the identity function a. Show that i is continuous <=> T' is finer than T. b. Show that i is a homeomorphism <=> T'=T This is all I've got. According to the first statement... X \subset T and...

Hi, I read the chapter "Anticommuting Numbers" by Peskin & Schröder (page 299) about Grassmann Numbers and now I would like to prove \int d \bar{\theta}_1 d \theta_1 ... d \bar{\theta}_N d \theta_N e^{-\bar{\theta} A \theta} = det A \theta_i are complex Grassmann Numbers...

Homework Statement Prove: csc2@= 1/(1-(sin@-cos@)^2 Homework Equations The Attempt at a Solution I'm stuck can't seem to work this on out. I'm not seeing the relationship between the two

Homework Statement Find the exact value of the expression Tan(3/4-12/5) Homework Equations tan(x-y)= (tan3/4 -tan12/5)/ (1+tan3/4tan12/5) The Attempt at a Solution I am not sure how to get exact values for these ratios. I haven't been able to get past this point

Homework Statement \bigtriangledown\times\\(v\times w)= v(\bigtriangledown\cdot w) - w(\bigtriangledown\cdot v)+ (v\cdot\bigtriangledown)w - (w\cdot\bigtriangledown) v I've tried expanding left side and get [v1(dw2/dy+dw3/dz)-w1(dv2/dy+dv3/dz)]i +...

Hi Everyone, Do there exist any explicit formula for Cos(x_1+x_2+...+x_n) as a sum of products of Sin(x_i) & Cos(x_i)? Or we need to expand using Cos(A+B), Sin(A+B) again & again? If it exists then what is about Sin(x_1+x_2+...+x_n)? [It is understood that there will be 2^(n-1) number of...

Homework Statement Differentiate the identity sin2x = 2sinxcosx to develop the identity for cos2x, in terms on sin x and cos x Homework Equations The Attempt at a Solution Im not sure where to start with this one. Should I find the derivative of both sides of the equation, and...

Homework Statement Show that (S, *) is a group where S is the set of all real numbers except for -1. Define * on S by a*b=a+b+ab The Attempt at a Solution Well I know that i have to follow the axioms to prove this. So I started with G1 which is associativity. This one I got to...

Homework Statement If A = I + uv*, where u and v are m vectors and A is known to be nonsingular, show that the inverse of A = I + \alphauv* where \alpha is a scalar value Homework Equations The Attempt at a Solution Since A is nonsingular, we know the rank of A is m. Since both...

Homework Statement Given S is a Skew-Hermitian (S*=-S), Prove that I - S is a nonsingular matrix Homework Equations If a matrix A is nonsingular, for Ax=0, x={0} The Attempt at a Solution (I-S)x=0, and I have been trying to show that the solution for x is always zero. Is this the...

I have seen the following identity used. Exp[iw/2]-Exp[iw/2]=Exp[iw]-1 I can't find this in any book and I can't prove it myself. The left side equals 2isin(w/2) The right side equals cos(w)+isin(w)-1 On the face of it, that seems to make the identity absurd How can one go about proving...

Hi everyone, Any assistance with this following problem would be greatly appreciated. I'm in Year 11 and working through Apostol volume 1. Homework Statement sin n*pi = 0, where n is an integer sin n*pi =/= 0, where n is not an integer. Prove these statements... Homework...

I am reading some notes and I can't understand a specif bit: the expression of the constant k_RP (RP means Reagents->Product) is as follows (Ξ is the heavyside function and C(t) the conditional probability): k_RP=dC(t)/dt=<Ξ_R[0]*(dΞ_P[t]/dt)>/<Ξ_R[0]> then for the following identity...

Homework Statement Basically I am finishing of a projectile question and I get stuck here: Trying to find \theta \frac{1}{2} (sin2 \theta) tan^2 \theta -tan \theta + \frac{1}{2} sin2 \theta = 0 Homework Equations The Attempt at a Solution I tryed spliting tan \theta into \frac{sin...

Homework Statement sinx cos2x=1 x is greater than or equal to 0 and less than 2pi Homework Equations What I used: 1-2sin2x cos2x-sin2x but there might be one that I didn't and should have... The Attempt at a Solution Basically I have...

I'm a pretty novice Physicist/Mathematician, but I've got a few offers for good universities, to show you my general level of knowledge. Could someone please explain in terms I will understand why this equation is considered so perfect and beautiful?

Ok, so a teacher showed an example in class awhile back. So I am going over my notes right now, and I don't understand a certain part of the problem. Also I am new to the forums and its my first time posting here, so please push me in the right direction if i make a mistake. integration of...

it is true in general that the sum (density of states for a physicst) \sum_{n=0}^{\infty} \delta (x- \gamma _{n}) is related to the value \frac{ \zeta '(1/2+is)}{\zeta (1/2+is)}+\frac{ \zeta '(1/2-is)}{\zeta (1/2-is)} here the 'gamma' are the imaginary parts of the non-trivial...

Homework Statement I am reading a book on relations on function and I am very confused with identity relation and function. Any help on understanding I relation and I function will be appreciated. Homework Equations A function from A to B is a relation f from A to B such that a) the...

Actually, the original motivation is to check the closure of SUSY \delta X^\mu = \bar{\epsilon}\psi^\mu \delta \psi^\mu = -i\rho^\alpha\partial_\alpha X^\mu\epsilon where \rho^\alpha is a two dimensional gamma matrix, and \psi^\mu ia s two dimensional Majorana spinor, the index \mu in the...

hi there! I´m doing vector analysis the last two weeks and I feel unsure about this identity. Can anyone of you say if I´m on the right way, and if not where my mistakes lie :) A_i(\vec r)=\sum_{j=1}^3R_{ij}x_j, R constant 3x3 matrix I have to calculate rot\vec A, rotrot\vec A...

Homework Statement sin^3(x) - cos^3(x) / sin(x) + cos(x) = csc^2(x) -cot(x) - 2cos^2(x) / 1 - cot^2(x) Homework Equations The Attempt at a Solution I have attached one of my many attempts. Any input?

Homework Statement Show that the LHS can be changed into the RHS. sec^6 x-tan^6x=1+3sec^2x tan^2x Homework Equations Trig identities. The Attempt at a Solution I tried factoring the LHS: (sec^2-tan^2)(sec^4+sec^2tan^2+tan^4) sec^2-tan^2=1 so that leaves me with the other...

Why is cos^2 x = \frac{1}{2} + \frac{cos(2x)}{2} ?

\equivHomework Statement Hi, I've been given a hyperbolic identity to prove: 2sinhAsinhB \equiv Cosh(A+B) - Cosh(A-B) Homework Equations Cos(A\pm B) \equiv CosACosB \mp SinASinB The Attempt at a Solution I have Cosh(A+B) and - Cosh(A-B) so i can kind of see that there will be...

Homework Statement I need help proving this identitiy. ...cos2A-cos4A tan3A = -------------- or tan3A = cos2A-cos4A/sin4A-sin2A ....sin4A-sin2A there both the same, just different way of writing it. please help! :) Homework Equations The Attempt at a Solution I honestly...

Homework Statement A cylinder contains one liter of air at room termperature and atmospheric pressure. At one end of the cylinder is a massless piston, whose surface area is 0.01 m^2. Suppose that you push the piston _very_ suddenly, exerting a force of 2 kN. The piston moves only one...

Homework Statement Prove the following identity: cos2A/1 + sin2A = cotA - 1 / cotA + 1 Homework Equations The Attempt at a Solution I proved the right side, which eventually lead up to cosA - sinA / cosA + sinA I have NO idea how to do the left side. I have wasted...

Does CSC(\pi/2 - x) = SinX OR 1 / SinX? What about CSC2(\pi/2 -x)? Does COT(\pi/2 + x) = -TanX or 1/-TanX?

Challenge to find a identity for the product abc, wherein each term contains a triangular variable as a factor and a, b, c are each separately used as the sole variable of the argument in at least one of the variable triangular numbers. My solution is abc = T_{(c+ab)} - aT_{b} - T_{c} -...

Is it possible to prove Euler's identity (e^i*pi = -1) without simply taking it as a special case of Euler's formula (e^i*x = cos(x) + i sin(x))?

Homework Statement sinX(1-2cos^2x+cos^4x)=sin^5x

Homework Statement tanX+tan Y / 1-tanXtanY= cotX+cotY/cotXcotY-1 Homework Equations tan= sin/cos cot= cos/sin The Attempt at a Solution

Homework Statement verify the identity : 1+sec(-∅)/sin(-∅+tan(-∅) = -csc ∅ Homework Equations The Attempt at a Solution 1+sec∅/-sin-tan∅ = -csc∅ I don't know where to start from, does anyone have any idea?

cosx/1-sinx + 1-sinx/cosx = 2secx + 2tanx I can get to 2secx + tanx - tanx, any help is appreciated