Identity Definition and 1000 Threads

Which trigonometric identitiy are used to transform 2(cos(x))^2+2cos(x)sin(x) into 0?

Homework Statement http://www.jyu.fi/kastdk/olympiads/2004/Theoretical%20Question%203.pdf http://www.jyu.fi/kastdk/olympiads/2004/Solution%203.pdf Question A- (b) They use some trigomentric identity that I don't understand, which one is it? Thanks in advance. Homework...

Hypothetically- If you were able to split in two like a bacterium, would you be two people with separate identities, or would you be one person living in two bodies?

Hypothetically- If you were able to split in two like a bacterium, would you be two people with separate identities, or would you be one person living in two bodies?

Can someone point me in the right direction with vandermonde's identity, I'm seeking a algebraic proof. essentially it its the sum of (a ,k)(b ,n-k) = (a+b ,n) when summed over k = 0 to n. Could someone right this out in latex since it is probably incomprehensible. I used (a ,k) to denote...

Homework Statement Is this correct (in the document)? The Attempt at a Solution I have a feeling it is not.

Question Statement If A+B+C = 180, prove that cos (A+B-C) + cos (B+C-A) + cos (C+A-B) = 1+4 cosAcosBcosC My Attempt If A+B+C=180, Then A+B-C=180-2C cos (A+B-c)=cos(180-2C) (After some substitution and caculation) cos (A+B-C) = -cos 2C Similarily, I obtain the same expression for...

Using the theorem that in any boolean ring a+a=0 for all a in boolean ring R. Then 0 is in R. Make the multiplicative identity 1 is also in it. Therefore R can only take 0 and 1 and no more because 1+1=0. 0+0=0. 1+0=1 always. So 2 or other elements can never occur.

Homework Statement hi, I'm working on constructible things again and in one of the proofs our prof threw out this identity and I just don't know where it came from...

Homework Statement If dU=TdS-PdV then (dS/dV)T=(dP/dT)V the T and V at the end means that T and V are constant How did they get this identity? It came from a thermodynamics hence for their notations. I have tried ways like rearranging but it dosen't seem to work. I think it has something to...

Homework Statement I am to show: closed integral {phi (grad phi)} X (n^)dS=0 Homework Equations The Attempt at a Solution I understand I am to use divergence theorem here.but cannot approach.Please help

Homework Statement Prove the Identity: tan²θ - sin²θ = tan²θsin²θ Homework Equations The Attempt at a Solution Well I got up to (sin²θ/cos²θ) - (sin²θcos²θ/cos²θ) = sin⁴θ/cos²θ I got the answer cause my calculator says sin²θ - sin²θcos²θ = sin⁴θ But I don't know how sin²θ - sin²θcos²θ =...

just wondering... does the parity operator squared give the identity operator?

Homework Statement Prove the following identity: (1 + cos \theta)^2 + sin^2\theta = 2(1 + cos \theta) Homework Equations cos^2 \theta + sin^2 \theta = 1 The Attempt at a Solution I've squared out the first bracket so that it becomes 1 + cos^2 \theta and multiplied out the second bracket so...

Can someone guide me on how to prove that F_{4n+3} + F_{4n+6} = F_{2n+1}^2 + F_{2n+4}^2 either side of the above is the difference (F_{2n+2}*F_{2n+3} + F_{2n+4}^2) - (F_{2n}*F_{2n+1} + F_{2n+2}^2) I intend to post this sequence F_{2n}*F_{2n+1} + F_{2n+2}^2, with a comment re a few...

I'm trying to solve this trig problem: sin^2000(x) + cos^2000(x) = 1 I'm not sure how to go about it... I tried starting with sin^2(x) + cos^2(x) = 1 and build up to 2000 but I didn't get very far. Obviously any multiple of pi will be an answer since either sin^2000 or cos^2000 will be...

Hi. I need to prove the following identity \arccos{z} =i \ln { z + (z^2 -1)^\frac{1}{2} } I was given a hint to write \cos{A}=z, then rewrite \cos{A} in terms of the exponential. \cos{A}=\frac{\exp{iA}+\exp{-iA}}{2}=z I took the log on both sides and got stuck at that...

I am having problems with one exam question. Does this diophantine equation have a solution(s) 12a+21b+33c=6 as far as I know this is not a linear equation, and what I read online says that Bezout identity only applies for linear diophantine equations. The solution says gcd(12,21,33)...

Homework Statement On the set of Natural Numbers from 1 to 10000 are given the following identity relations. R1 ; n R1 m where m and n have the same remainder by division by 24, that is mod n 24 == mod m 24. R2 ; n R2 m where n and m have in decimal notation the same number of 2s R3; n...

In my book, (cos4x)^2 is written 1+cos8x without referring to any formula. Which trig. identity is used here?

Can anyone help me solve the following problems? sec theta -1/1-cos theta = sec theta tan (pie/2 - theta) tan theta =1 Thanks

Hi can someone help me prove this identity? I'm having trouble understand the role of the interior product or more precisely how to calculate with it. My professor uses the "cut" notation _| but i don't see this in any textbooks. Can someone give me some hints on how to prove the identity?

(1-xt)/(1-2xt+t^2)=sum(Tn(x)t^n) How can i prove this equation? Could you give me a hint or suggestion?

Homework Statement Use the thermodynamic identity to derive the heat capacity formula C_V=T\frac{\partial{S}}{\partial{T}}_VHomework Equations C_V=\frac{\partial{U}}{\partial{T}} T=\frac{\partial{U}}{\partial{S}} dU=TdS-PdV+\mudN The Attempt at a Solution I used...

Homework Statement Show that, for any two nonzero complex numbers z_1 and z_2, \text{Log } (z_1 z_2) = \text{Log } z_1 + \text{Log } z_2 + 2 N \pi i \, , where N has one of the values -1, 0, 1. Homework Equations The logarithm on the principal branch is: \begin{align*}...

There is one last problem i have on my trig assignment and i have no clue how to do it. The questions is: Find sinx, cosx, tanx, sin2x, cos2x, and tan2x from the given information: secx=5, sin is negative. If anyone could show me how to do this problem it would be soooo appreciated...

Hey I've got an assignment on trig identities and can't figure this one out. Prove the Identity: tanx+cotx=2csc2x I got to tanx+cotx= 1/2 sin2x=1/4sinx2cosx but when i get to the point where i have numbers in front of the sinx or cosx i don't know what to do. Thanks for any help

Today the professor wrote down the following for use in an integral: \frac{1}{2}cos(2\theta)=sin\theta cos\theta i am not sure is this is correct. i have tried to prove this and cannot, i have also not found it in an table of trig identities. Is this a valid identity? i am not sure since...

Question: If \hat{A} and \hat{B} are two operators such that \left[\hat{A},\hat{B}\right] = \lambda, where \lambda is a complex number, and if \mu is a second complex number, prove that: e^{\mu\left(\hat{A}+\hat{B}\right)}=e^{\mu\hat{A}}e^{\mu\hat{B}}e^{-\mu^{2}\frac{\lambda}{2}} What I...

Is there a non-ugly proof of the following identity: \langle Ax,y \rangle = \langle x,A^*y \rangle where A is an nxn matrix over, say, \mathbb{C}, A* is its conjugate transpose, and \langle \cdot , \cdot \rangle is the standard inner product on \mathbb{C} ^n.

This isn't a homework question, it's just for personal enrichment. I've been trying to prove that \tan\frac{\theta}{2}=\frac{\sin\theta}{1+\cos\theta} I tried starting off with \tan\frac{\theta}{2}=\frac{\sin\frac{\theta}{2}}{\cos\frac{\theta}{2}} is this even the right way to start the...

tan3A= 3tanA-tan3A/1-3tan^2 A

could anyone explain (no calculation) how to work the following identity so could get an understanding of it thank you tan(45+A)degrees tan(45-A)degrees=1

can anyone help[ me prove the following identity i keep on ending up in a dead end tan3A=3tanA-tan^3 A/ 1-3tan^2 A thank you

Hey all, I am unsure how to do this problem... i find problems where i have to derive things quite difficult! :P http://img143.imageshack.us/img143/744/picture2ao8.png this is the Full Fourier series i think and so the Fourier coeffiecients would be given by...

Hi, I am trying to prove \frac{tanx+1}{tanx-1}=\frac{secx+cscx}{secx-cscx} I am working on the right side and trying to get it to the same form as the left side. I get to \frac{1+2sinxcosx}{sin^{2}x-cos^{2}x} which I COULD apply the fact that sin2x=2sinxcosx as well as...

Hi, how do I interpret the last sum: http://planetmath.org/encyclopedia/LagrangesIdentity.html Sum (...) 1<=k < j <= n Is it the double sum: Sum( Sum( (a_k*b_j - a_j*b_k)^2 from k = 1 to n) from j = 2 to n ) ?

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...