Identity Definition and 1000 Threads

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

should the subring inherit the same multiplicative identity of the original ring? assuming multiplicative identity is required in the definition of ring. according to the book (Rotman's), 1\in S is required. But, does it mean S contains the same multiplicative identity, or contains its own...

Homework Statement cos(squared)x = sinx-1/2 Homework Equations cos(squared)x= 1-sin(squared)x The Attempt at a Solution I tried everything but my answer does not match my answers in calculator

If I have ABCXC^-1A^-1B^-1=I (that is C, B, A inverse), can I modify the order so that the AA^-1, BB^-1 are multiplied to get the identity matrix so that I can get it down to X=I?

Homework Statement If S = {s in R such that s=/=1} is an abelian group under circle operation (Circle Operation a*b = a + b -ab for a, b in R) then R is a field Homework Equations The verification of the field axioms The Attempt at a Solution The field axiom that I'm struggling to...

[SOLVED] A Trigonometric Identity Probelm If I have sin^2 2x would I be able to apply the identity sin^2x = (1/2)(1-cos2x) to get this: sin^2 2x = 2(1/2)(1 - cos^2 x) Similarly, if I had sin^2 2x + cos^2 2x would I be able to use the identity sin^2 x + cos^2 x = 1 to get: sin^2 2x +...

From what I was reading, the apparent definition goes as: The Identity Function on E is the function IE from E into E defined by IE(x) = x. Since IE is the set of all ordered pairs (x,x) such that x ϵ E, IE is also called the diagonal subset of E x E. If f is a function from E into F, clearly...

I am having some difficulty with identity matrices in linear algebra at the moment. I am sure it is fairly simple to solve, but I just cannot follow the logic behind this particular problem. I need to come up with a matrix B (2x2), such that B =/= I but B2 = I Since I = (1 0) (0 1)...

[FONT="Times New Roman"]Homework Statement find arc length of the segment of the 2space curbe that is defined by the parametric equations x(t) = t-sin(t) y(t) = 1+cos(t) 0 ≤ t ≤ 4π The Attempt at a Solution [FONT="Times New Roman"]I've found dx/dt and dy/dt respectively and put them...

Homework Statement For positive integers n, r show that C(n+r+1, r) = C(n+r, r) + C(n+r-1, r-1) + ... + C(n+2, 2) + C(n+1, 1) + C(n, 0) = C(n+r, n) + C(n+r-1, n) + ... + C(n+2, n) + C(n+1, n) + C(n, n) Homework Equations The Attempt at a Solution

Homework Statement In S_3, show that there are four elements satisfying x^2=e and three elements satisfying y^3=e. The Attempt at a Solution I don't understand what the question is asking at all...

Hello all, I have a question I'm having a hard time with in an introductory Algebraic Topology course: Take two handlebodies of equal genus g in S^3 and identify their boundaries by the identity mapping. What is the fundamental group of the resulting space M? Now, I know you can glue two...

deriving identity - need help! Homework Statement Derive for S^{p}_{n} = 1^p + ... + n^p the identity (p+1)*S^{p}_{n} + (p+1 choose 2)*S^{p-1}_{n} + ...+S^{0}_{n} = (n+1)^(p+1) - 1 Homework Equations Um, I know that the S^{1}_{n} = n(n+1)/2 S^{2}_{n} = n(n+1)(2n+1)/6 S^{3}_{n} =...

Homework Statement Prove that \frac{cos 3x}{cos x} = 2cos (2x) - 1 Homework Equations The ones I used: cos 2x = cos^2 x - sin^2 x sin^2 x + cos^2 x = 1 The Attempt at a Solution I *think* that the left hand side cannot be manipulated so I only fooled around with the right hand side...

yet another trig identity... Homework Statement prove: cos^(x)= 5/16+15/32(cos2x)+3/16(cos4x)+1/32(cos6x) Homework Equations The Attempt at a Solution i attempted to use the formula cos^2(x)=(1+cos2x)/(2), and square both sides, then use it again for the square roots, then...

Homework Statement im in first year differential calculas and i have no idea what my prof wrote down...i just copied it and thought ide figure it out later. but i can't fore the life of me. Homework Equations the identitie that he wrote is: sinC+sinB=2Sin (C+D)/2 cos (c-D)/2 The...

Homework Statement The problem is written as: Del X (A X B) = (B*DEL)A- (A*DEL)B +A(DEL*B) -B(DEL * A) where * = dot. I don't know how to evaluate this because if the author meant for the standard mathematical order of operations to apply it makes since they wouldn't have worried about...

I ran across this identity in some actuarial literature: Pr( (x_1 \le X \le x_2) \ \cap \ (y_1 \le Y \le y_2) ) = F(x_2, y_2) - F(x_1, y_2) - F(x_2, y_1) + F(x_1, y_1) First of all, I am not certain this is correct. I think the expression on the LHS is equal to the following double...

Homework Statement If \frac{(cos x)^{4}}{(cos y)^{2}}+\frac{(sin x)^{4}}{(sin y)^{2}}=1 prove that \frac{(cos y)^{4}}{(cos x)^{2}}+\frac{(sin y)^{4}}{(sin x)^{2}}=1 The Attempt at a Solution (cos x)^{4} (sin y)^{2}+(sin x)^{4} (cos y)^{2}=(sin y)^{2}-(sin y)^{4} On...

Homework Statement http://img206.imageshack.us/img206/9099/titleol2.jpg http://g.imageshack.us/g.php?h=206&i=titleol2.jpg Show the above statement is equivalent to : sec (2x) + tan (2x) Homework Equations The Attempt at a Solution First attempt in which I used the...

Homework Statement sin5xcos3x=sin4xcos4x+sinxcosx, solve the identity Homework Equations all the identities and formulas mentioned in my last thread. The Attempt at a Solution Alright so I thought I could use the product to sum formula on the left side which ended up being...

How does y = e^(x(1-i)) + e^(x(1+i)) work out to y = (e^x)sinx + (e^x)cosx? Using Euler's identity I get, y = (e^x)e^-ix + (e^x)e^ix y = e^x(cosx - isinx + cosx + isinx) y = e^x(2cosx)

Homework Statement Verify the possibility of an identity graphically. (Completed this part) Then, prove each identity algebraically. \dfrac{sinx+tanx}{cosx+1}=tanx Homework Equations tan\theta=\dfrac{sin\theta}{cos\theta} cot\theta=\dfrac{cos\theta}{sin\theta}...

Homework Statement Let l, m, and n be positive integers with l \leq m and l \leq n. Prove the identity. (\stackrel{m + n}{l}) = (\stackrel{m}{0})(\stackrel{n}{l}) + (\stackrel{m}{1})(\stackrel{n}{l-1})+...+(\stackrel{m}{l})(\stackrel{n}{0}) 2. The attempt at a solution I have no clue, I...

Homework Statement Prove the following identity by mathematical induction: \sum_{i=1}^n \frac{1}{(2i - 1)(2i + 1)} = \frac{n}{(2n + 1)} Homework Equations The Attempt at a Solution Let P(n) = \sum_{i=1}^n \frac{1}{(2(1) - 1)(2(1) + 1)} = \frac{1}{(2(1) + 1)} P(1) =...

Can u guys tell me the difference b/w an Equation and an Identity? Thx

Homework Statement I'm attempting to prove that 1 - sin^2 t /(1 + cos t) - cos^2/(1+tan t) = cos t sin t 2. The attempt at a solution I've tried various approaches. The most promising has the LHS reduced to: (sin t cos t (1 + cos t + sin t cos t))/((1 + cos t)(cos t + sin t))...

Prove that a matrix A is invertible if and only if its reduced row echelon row is the identity matrix.

Im supposed to verify that (1-sinx)/(1+sinx) = (secx-tanx)^2 RHS = (secx-tanx)^2 = (1/cosx - sinx/cosx)^2 = [(1-sinx) / cosx]^2 = [(1-sinx)(1-sinx)]/cosx^2 = (1-2sinx+sinx^2)/(1-sinx^2) From here, I'm feeling pretty confused. I'm not even sure if all my values are correct.

I'm having difficulties with a few identity problems and I wanted to make sure I'm doing the ones I believe I did correctly, correctly... 1. (cos^3x)+(sin^2x)(cosx) (cosx)(cos^2x)+(sin^2x)(cosx) 2cosx 2. (1+cosy)/(1+secy) (1+cosy)/(1+1/cosy) (1+cosy)/(1+cosy) 1 3. (tanx)/(secx)...

can anybody give me the definition of a trig-identity? And then the definition of an equation? Because i think that the relation \tan^2 x + 1 = \sec^2 x is not an identity.