Identity Definition and 1000 Threads

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: J-3/2 (x)=\sqrt{\frac{2}{\pi x}}[\frac{-cos(x)}{x} - sin(x) ] Main reason is \Gamma(n-3/2+1) give a negative value for n=0 and possitive value for n=1,2,3... I cannot find a series representation of this gamma...

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) = SUMn=0[ (a)n * z^n ] / [ (b)n * n!] where (a)n is the Pochhammer symbol and is defined by: a(a+1)(a+2)(a+3)...(a+n-1)...

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...

Hello, I have to write an essay on the poem "Theme for English B" by Langston Hughes. The topic is is it crippling to question one's identity or is it ultimately enabling? I have trouble understanding the topic. Could anyone give me a general idea on what to write about?

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...

For a set S, there is an identity element e with respect to operation * such that for an element a in S: a*e = e*a = a. For a matrix B that is m x n, the identity element for matrix multiplication e = I should satisfy IB = BI = B. But for IB, I is m x m, whereas for BI, I is n x n. Doesn't...

I have been trying to familiarize myself with a particular system of first-order logic with identity, in which the process of substitution is achieved by replacing, one at a time, one occurrence of a variable with a term. (see axiom schemes 6) and 7)). I want to use these axioms to prove the...

1. Homework Statement [/b] f _{a} (z) is defined as f(z) = 1 + az + \frac{a(a-1)}{2!}z^{2}+...+\frac{a(a-1)(a-2)...(a-n+1)}{n!}z^{n} + ... where a is constant Show that for any a,b f _{a+b} (z)= f _{a}(z)f _{b}(z) Homework EquationsThe Attempt at a Solution I've tried starting directly...

Homework Statement http://carlodm.com/images/m.png Homework Equations sin2 et + cos2 et = 1 The identity above is foreign to me. Can anyone explain/have external links that explains this identity? I haven't seen anything like it and Google isn't showing anything useful. Thanks

Homework Statement Show that if p\in (1,\infty) the identity functions id:C^{0}_{1}[a,b]\longrightarrow C^{0}_{p}[a,b] and id:C^{0}_{p}[a,b]\longrightarrow C^{0}_{\infty}[a,b] are not continuous. Homework Equations C^{0}_{p}[a,b] is the space of continuous functions on the [a,b] with...

1. Find the limit of [Cos(x+h)-Cos(x)]/h as h approaches 0 2. Solve using trig identity cos(A+B)= cos(A)cos(B)-sin(A)sin(B) 3. My first class using the actual definition of a derivative. My high school teacher just showed us the shorthand and said "good luck when you get to...

Homework Statement Regarding the identity Ax(BxC) Homework Equations Does this identity only hold when A != B != C?

I noticed that the graphs of sin(x) and sin(x) ^ 2 are very similar. So I offset sin(x) ^ 2 to exactly match sin(x): sin(x) = 2 sin^{2}\left(\frac{x}{2} +\frac{\pi}{4}\right) - 1 Is this right, or is it an illusion? I haven't been able to find any identity that this is based on. If it is...

Is there a name for studying a Lie "group" that doesn't use the identity matrix as a member of the group? I know it's not technically a group anymore, but is there any mathematical work pertaining to the general idea... and what is the terminology so that I can research it better?

Homework Statement div(grad f x grad g)=0. I need to prove this somehow. Homework Equations The Attempt at a Solution I don't really know where to even start this at >.< any help is greatly appreciated.

Homework Statement Derive sin^2 + cos^2 = 1 Homework Equations Use cos 0 =1, cos (x+y) = cos x cos y - sin x sin y Earlier someone posted this same question, but I still don't understand it so please help

1. cos(2x+y) = cos(a+b) = sinasinb + cosacosb = (2x+y) = sin2xsiny + cos2xcosy = sin2x = 2sinxcosx and cos2x = cos2x-sin2x = cos(2x+y) = (cos2x-sin2x)cosy - (2sinxcosx and cos2x)siny (is this correct) 2. evaluate the following exactly (use \sqrt{} in your answer where necessary) cos...

I have been reading papers for my research and I came across this equation twice: \lim_{\eta\to 0+}\frac{1}{x+i \eta} = P\left(\frac{1}{x}\right) - i \pi \delta(x) Where P is the pricipal part. It has been quite a while since I have had complex variables, but might it come from the...

Homework Statement I do not know if the following is correct;if it is,I will be able to save some calculation while doing a problem.Can you please let me know if it is true: \epsilon_{ijk}\*\epsilon_{lmn} = \left(\begin{array}{ccc}\ g_\ {11}&\ g_\ {21}&\ g_\ {31}\\ g_\ {12}&\ g_\...

Two sets are equal iff they contain the same elements. I would argue that two sets that have the same elements are identical as well as equal and that there is a difference between identity and equality. In general {2,3}={3,2} if neither set is defined to be ordered. However obviously {5} \neq...

I was doing a signals and systems problem and I think I might be screwing something up with the cosine function because I get cos(a+b) = cos(a)*cos(b) This is how cos(a+b)=Re\left\{ e^{j*(a+b)} \right\} =Re\left\{ e^{j*(a)}*e^{j*(b)} \right\} =cos(a)*cos(b) Can anyone point out my mistake...

I found this equation last night on Wolfram: http://functions.wolfram.com/ZetaFunctionsandPolylogarithms/PolyLog/06/03/0001/ How is it possible this equation has no restrictions given that the gamma function has poles at the negative integers? Also, won't the zeta function portion run...

If I have a semigroup S, is it possible to partition the set of element S into two semigroups S_1 and S_2 (with S_1 \cap S_2 = 0), in such a way that S_1 has an identity element but S_2 has none?

I forget how this one goes. A cos(x) + B sin (x) = C sin (x + invtan(?)) How do you go about condensing both these terms into 1 like the above?

Homework Statement Prove this is an identity: sin2(x)-sin2(x)=sin(x+y)sin(x-y) Homework Equations N/A The Attempt at a Solution I have made a lot of attempts but can not get one side to equal the other. I know It's something really simple I am missing, but can't figure it out.

From Euler's identity: i^i=exp(-pi/2)= 0.2079 (rounded). I've always thought of this as an interesting result although I don't know of any particular significance or consequence of it. Is there any?