Identity Definition and 1000 Threads

Is this identity true? gcd(a, lcm(b,c)) = lcm(gcd(a,b), gcd(a,c))

Hi, I have a question about a problem: 1/2csc(THETA)sec(THETA) I have to find the identity for it and I know that csc is 1/sin and sec is 1/cos but after that I don't see where it can lead to a simple answer. If anyone knows it would be helpful, thanks!

It seems to me that this problem is going to become a major issue sooner than later. Not soon enough in my opinion considering no one is doing anything about it. Much as I would like these people summarily executed without trial, the problem will unfortunately have to get much worse before...

I am asked to prove the following: (Note: z = x + iy) |cos(z)|2 = cos2x + sinh2y --------------- So I started the following way: |cos(z)|2 = |cos(x+iy)|2 = |cos(x)cosh(y) - i(sin(x)sinh(y))|2 = cos2(x)cosh2(y) + sin2(x)sinh2(y) [after having square root squared removed] once I got here I...

Is the identity matrix (or multiple of) the only one that commutes with other matrices or are there other matrices that AB=BA? Thanks

Problem: #29 in Strang Linear Algebra Prove that the identity matrix cannot be the product of 3 row exchanges (or five). It can be the product of 2 exchanges (or 4). Now, to start, we try to count the number of rows that are different from the identity matrix. For the first row exchange, it's...

T^i K_{ij} = K T^j K^{-1} repeated indices imply summation. T^i are the generators (Lie algebra elements) of SO(3). i.e.T^i_{jk} = - \epsilon_{ijk} T^i \in so(3) K \in SO(3) How to show it's true? Is there a universal formula for all Lie group?

Hi Where is the error is this 'identity'?: (-e^i)^{\frac{1}{2}} = (-1)^{\frac{1}{2}}*e^{\frac{i}{2}} My calculator says that the right side is minus one times the left but I can't see the mistake I'v made. Help me please, thanks.

Hi, As in the title, what's the difference between the Kronecker delta and the identity matrix? They seem to have the exact same definition, so why are they differentiated? Thanks. Molu

how do i prove the next identity: 999/1000=1/(2!)+2/(3!)+3/(4!)+4/(5!)+5/(6!)+1/(7!)+7/(8!)+6/(9!)+1/(10!)+2/(11!)+2/(12!)+5/(13!)+2/(14!)+12/(15!)?

One often encounters the following identitiy in Tensor Analysis/Differential Geometry: dx^j (partial/partial x^i) = partial x^j / partial x^i = delta ij It's easy to see why partial x^j / partial x^i = delta ij but how does dx^j (partial/partial x^i) = partial x^j/partial x^i ? I...

Hi, I'm stuck another vector identity question. It's of a different kind to the other one I asked about and looks so much easier but I just can't see what I need to do. I am told to use standard identities to deduce the following result. The standard identities being referred to are listed in...

Hi, I am having an immense amount of trouble trying to show that the following identity is true. Q. Let F be a C^2 vector field. Prove that \nabla \times \left( {\nabla \times \mathop F\limits^ \to } \right) = \nabla \left( {\nabla \bullet \mathop F\limits^ \to } \right) - \nabla ^2...

how can i prove tan X/sinx+cosx=sin^2 X + sinXcosX/cos X - 2cos^3X so far I've tried using basic identities to figure it out, but i just end up getting confused. :confused:

figured it out thanks!

For homework, we were asked to prove that \cos^2 \theta + \sin^2 \theta = 1 is true for all angles \theta . Can someone please take a look at these and let me know if they are acceptable. I'm pretty sure the second one works, but I'm not sure of the first one, mainly because the premise of...

for phasor, v = 20V e^(-j60) and i = 0.5A e^(-j30) how can i write them in v(t) and I(t) ?? pls help thanx

Trigonometric Identity?? I just can't figure this out. I don't think I've covered enough material to do this. Can anyone help? I've put the entire question but I am sure all i need is a little explanation and maybe the first answer and i could do the rest. :confused: Let z =...

does anybody know the identity for |sinx-siny| and |cosx-cosy|?

Hi, can someone give me some assistance with the following questions? 1. Let f(x,y,z), g(x,y,z) and h(x,y,z) be any C^2 scalar functions. Prove that \nabla \bullet \left( {f\nabla g \times \nabla h} \right) = \nabla f \bullet \left( {\nabla g \times \nabla h} \right) . 2. Let S be the...

"Let f[a,b]->[a,b] be continuous. Prove that there exists at least 1 x in [a,b] such that f(x)=x." This seems simple geometrically since if we consider the identity function g(x)=x, if f(x) is continuous, then if you "draw" the graw of f, it must intersect g at some point. At that point...

I've wracked my brains out trying to prove this identity. If anyone could offer some suggestions, I'd greatly appreciate it! (sin(x))^4+(cos(x))^4 = 0.25∙cos(4x)+0.75

Hello, I need some help on this vector identity. I am supposed to prove that Del Dot (Del(g(r)))=(2/r){dg(r)/dr}+(d^2g(r)/dr^2). Using Cartesian Coordinates. Any help would be GREATLY appreciated> :)

Just working through my FP1 book and have got stuck on a question. Use the identity (r+1)^3 - r^3 \equiv3r^2 + 3r + 1 to find \sum\limits_{r = 1}^n r(r+1) I've tried using the method of differences to get n^3 + 3n^2 + 3n, but can't see how to get it back into its original form, not sure how...

Hello, I need to prove (7) here: http://mathworld.wolfram.com/DeltaFunction.html http://mathworld.wolfram.com/images/equations/DeltaFunction/equation5.gif The instructions were to start with the definition of the delta function by integral, and then chagne variables u -> g(x). But I...

Ive been trying to prove this identity for the past hour, and I can't seem to do it. I am starting to think its not possible. Heres the identity. sin2x/1-cos2x = cotx Can anyone give me some kind of hint. :frown:

Hi, I am trying to find the tangent space of SL(n,real) where A(0) is defined to be the identity matrix. First of all I worked on the case when n=2 and found that the tangent space was A = \left( \begin{array}{ccc} a & b \\ c & -a \end{array} \right) where a,b,c belong to the...

Can someone explain to me why for any operator A and functions f(x), g(x), (Af(x))^*g(x) = f^*(x)A^+g(x) Where "^+" denotes the hermitian conjugate of A. I went to see the demonstrator about it and he couldn't explain/prove that result. Thx.

Prove the identity \int_{\partial D}\phi \nabla \phi \cdot \n \ds = \int \int_{D} (\phi \nabla^2 \phi + \nabla \phi \cdot \nabla \phi) \dA Can I just let \phi be equal to P + Q, substitute into the left side, and try to derive the right side? This is a weird looking identity by the way.

I tried to prove div(F x G) = G.(curlF) - F.curl(G) and ended up getting the right hand side equaling twice the left hand side, with no idea where i'd gone wrong :( can someone show me how to prove it correctly? and, if you have time.. see if you can pick where i went wrong? this...

Prove the identity: sinA / (1+cosA) = tan (A/2). Im going no where with this, please help?:confused: :confused:

Please help me prove this identity: 1/(cosA+sinA) + 1/(cosA-sinA) = tan2AcosecA I got as far as LHS= 2cosA/cos^2A - sin^2A. I can't go any further, please help!:confused:

1 - \frac{\cos^2 \theta}{1 + \sin^2 \theta} = \sin \theta I can only get to \frac{2\sin^2 \theta}{1 + \sin^2 \theta} and I don't know if that's correct.

I have been set an exercise from my textbook to do for homework but I am having some problems on one of the questions, I havn't encountered any of this type before and I am quite stumped. "Eliminate \theta from equations x=2+\csc\theta and y=\frac{1}{4}\tan\theta" So I am guessing I start...

Can someone please help me establish this identity? \cos \theta (\tan \theta + \cot \theta) = \csc \theta

Someone told my friend, who in turn told me that this identity was true. However, I can't prove it, and when I try to use it I can't get the right answer to a rather simple problem. So, is it true that \frac{1}{2} + \sum_{j=1}^n cos(jx) = \frac{sin([n+\frac{1}{2}]x)}{sin(\frac{x}{2})} ?? Thx!

Hello, I am having trouble with particular algebra question. I don't know where to start and it would be greatly appreciated if someone could point me in the right direction. Here is the questoin: Let V be a vector space, where T is a linear map of V prove if T^2 = 0 then I - T is...

I ran into this trig identity trying to do my physics hw: a*cos(s)+b*cos(t) I tried deriving it using an analogous approach to deriving the product-sum trig identity, but ran into problems. I was wondering if this trig identity exists, or if I should just try to find some clever way to...

When we say that the identity and inverse element in a vector space is unique, does it mean that those elements are the same for all x in V? or does it mean that each x has its own unique identity or inverse element? moreover, is there a geometric way of explaning what a field is? because I...

If a tree falls with no one around then there should be the presence of sound waves. Sound, nonetheless, is a product of the brain and a element of consciousness and would not be present if there is no one to hear. Perception is not the thing perceived. When dealing with the mystics claim of...

I'm writing a program that likes to test for equality simply by checking identity: IOW, a.equals(b) iff a == b. Now, I think I would like to use HashMap's and stuff... so I would like to be able to use the appropriate accompanying hashCode method... that is, the default implementation of the...

yes well I got the last problem...but I still want to have an idea were the identity siny+sinx=2sin(x+y)/2cos(x+y)/2 came from please someone sort of explain please! thanx

[FONT=Comic Sans MS]undefinedundefinedundefinedneed help=====) (sin2x+sin4x)/(cos2x+cos4x)=tan3x

Let \vec A be an arbitrary vector and let \hat n be a unit vector in some fixed direction. Show that \vec A = (\vec A .\hat n)\hat n + (\hat n \times \vec A)\times \hat n.

Hello everyone! I'm trying to prove the following identity, but I'm not very lucky in finding the proof: :eek: {{n+k-1}\choose{n-1}} = \sum_{i=1}^k {k-1\choose i-1}{n\choose i}\,\, 1\leq k \leq n I've tried to interpret this as a combinatorial problem, and I know the left hand...

I am trying to solve an exercise from MTW Gravitation and the following issue has come up: Let D denote uppercase delta (covariant derivative operator) [ _ , _ ] denotes the commutator f is a scalar field, and A and B are vector fields Question: Is it true that [D_A,D_B]f = D_[A,B]f ?

Can someone help me how to deal with this identity that i must prove? {n + k-1 \choose n - 1} = \sum_{i=1}^k {k-1\choose i -1} {n \choose i} I've tried to figure out what the combinatorial meaning of the right hand side is, but I didn't succeed :(

Hello All I am having problems Verifying this identity (COS A) / (1-SIN A) = SEC A + TAN A I can get the RHS = (1 + SIN A)/COS A But this does not equal the LHS Any advice is welcome. THanks

F(x+dx)=F(x)+F'(x)dx is the above eqn an identity or something?can someone explain to me what is happening in this eqn?

For my chem class my teacher is going to give us 2 unknowns and we have to find out their identity. How would you do this? I figured that you would heat the liquids to figure out their boiling point and then look in the book (she'll let us use the books) to figure out the substaNce. I...