Identity Definition and 1000 Threads

1 + 1 = 2 sec2x ______ ________ 1+sinx 1-sinx PLEASE SOMEONE HELP! UGH! In case you can't tell what that says, it's 1/1+sinx + 1/1-sinx = 2sec2x​

I was thinking about identities, and seem to have arrived at a contradiction. I'm sure I'm missing something. A(n) (two-sided) identity for a binary operation must be unique. I will reproduce the familiar proof: Proof: Suppose a is an arbitrary element of a set S, e and e' are both...

I need to verify the given identity. I've tried every which way i can think of, but can't figure this one out. I am self-studying this book "College Trigonometry 5th Edition by Aufmann. This is exercise set 3.3, problem 63. cos^2(x) - 2sin^2(x)cos^2(x) - sin^2(x) + 2sin^4(x) = cos^2(2x)...

\frac{2 i}{(2 i + 1)!} = \frac{1}{(2 i)!} - \frac{1}{(2 i + 1)!} Could anybody please show what it is that needs to be done on LHS to get to RHS in this identity.

i am completely lost as to how to go from p^ \frac{1}{m}∇p to \frac{m}{m+1} ∇p^\frac{m+1}{m}

Homework Statement Prove the identity. Homework Equations http://postimage.org/image/vjhwki1ax/ The Attempt at a Solution http://s13.postimage.org/jkhubi4lz/DSC03534.jpg

I got trouble to understand the cyclic sum identity (the first Bianchi identity) of the Riemann curvature tensor: {R^\alpha}_{[ \beta \gamma \delta ]}=0 or equivalently, {R^\alpha}_{\beta \gamma \delta}+{R^\alpha}_{\gamma \delta \beta}+{R^\alpha}_{\delta \beta \gamma}=0. I can understand the...

Homework Statement I'm trying to understand a proof of the LC-KD identity involving determinants (see attachment), from the book Introduction to Tensor Calculus and Continuum Mechanics by Herinbockel. What is the author saying in the last line of text? How can we sum the deltas in the upper...

I look for trig identitiy to simplify this expression: \frac{\sin(nx/2)}{\sin(x/2)} is there one specficic to use, or is there other ones that will help to simplifiy? I have been trying but can't make it simplier! Thanks!

Homework Statement To prove that \sum over m=1 to 15 of sin(4m-2) = 1/4sin2, where all angles are in degress Homework Equations The Attempt at a Solution Tried to solve it using identity sinx+siny=2sin((x+y)/2)cos((x-y)/2)..but all attempts failed..help

Hi, I'm looking for intuition and/or logic as to why we would want or need morphisms according to axioms in category theory, to imply that in the category of rings, they must preserve the identity (unless codomain is "0"). Thank you very much.

Homework Statement sin4x=(4sinxcosx)(1-2sin^2x) Homework Equations Trig identities. The Attempt at a Solution sin4x=(4sinxcosx)(1-2sin^2x) (4sinxcosx)(cos2x) stuck right here...

Homework Statement Prove sin(x-iy) = sin(x) cosh(y) - i cos(x) sinh(y) Homework Equations The Attempt at a Solution I tried to prove it by developing sinh into it's exponential form, but I get stuck. sinh(x-iy) = [ ei(x-iy) - e-i(x-iy) ] /2i = [ eixey - e-ix e-y ] /2i...

Homework Statement Show that : 1 + cos(2∏/5)= 2 cos(∏/5) Homework Equations cos(2x) = cos^2(x)-sin^2(x) cos^2(x)+sin^2(x) = 1 The Attempt at a Solution I have tried using the two formulas above but i couldn't show the required result.

Homework Statement In a worked example I have of an integration it states the integral of (cosx)^2 = the integral of (1 + cos2x)/2 How is this equality reached? Is this a known identity, (cosx)^2 = (1 + cos2x)/2 ? Thank you. Homework Equations The Attempt at a Solution

Homework Statement I'm trying to follow some solution to an exercise in physics and apparently e^{-im \frac{3\pi}{2}}=i^m where m \in \mathbb{Z}. I don't realize why this is true. Homework Equations Euler's formula.The Attempt at a Solution I applied Euler's formula but this is still a...

I am trying to understand Derek Parfit view on persistence of personal identity. You don’t have to take in weird examples such as branching. Can you also show some of the flaws of his view. Can you advice?

This isn't a homework problem, but it won't let me post on the other page. A well known vector identity is that rot(rot(E)) = grad(div(E)) - div(grad(E)). I've actually used this before without encountering any problems, so I don't know if I'm just having a brain fart or something, but...

Homework Statement Here is the question given: A blade for a lawnmower consists of two parts made of the same material and joined together as shown: The length OP is one unit in length and MPQN is square in shape. Develop an equation for the cross-sectional area of the blade and...

Homework Statement Prove that: tan^2∅/tan∅ - 1 + cot^2∅/cot∅ - 1 = 1 + sec∅cosec∅ Homework Equations The Attempt at a Solution I have solved the question taking tan∅ = sin∅/cos∅. But I want to solve it some other way.

So it is true that ei∏+1=0. But what does this mean? Why are all these numbers linked?

Homework Statement This was a problem on our final. I played with traits of a bijection to no avail and got a 0%. It's got me completely stumped. I really cannot even figure out a way to start. Let X be a finite set. Let f : X → X be a bijection. For n ε Z>0, set fn = {f°f...°f} n times Prove...

When I was checking my work, Wolframalpha took my trig work a step further with an identity that no one in my Calculus II class has ever seen, including my teacher. csc(2x) - cot(2x) = tan(x) I tried to prove the identity myself and I looked online, but no luck. Please, could someone...

I have been working on showing the equality between N=0 to ∞ Ʃ cos(2nθ)(-1)^n/(2n)! = cos(cos(θ))cosh(sin(θ)) I started by using the standard series for cosine and putting cos(2nθ) in for the x term. I did the same for cosh(sin(θ)). I manipulated the forms every way I could think but...

it's bothering my brain..i thought about it many times...i can't make intuition of it can anyone prove it? oh by the way... C = Sqrt[A^2 + B^2] and theta is equal to arctan(B/A)

Let f be an analytic function defined in an open set containing the closed unit disk and let z in ℂ be fixed. I've simplified a more complicated expression down to this identity, and as implausible as it looks, after some numerical checking it does in fact appear to be true, but I can't find a...

Homework Statement Write the following in terms of the cofunction identity: cos(4pi/3) Homework Equations I know the θ is in Quadrant 3, but my question is, which cofunction identity am I suppose to use? Cofunction Identities: cosx = sin(pi/2 - x) #1 cosx = sin(pi/2 + x) #2...

Hello! I'm want to prove a vector identity for (\nabla \times \vec{A}) \times \vec A using the familiar method of levi-civita symbols and the identity \epsilon_{kij}\epsilon{kmn} = \delta_{im}\delta_{jn} - \delta_{in}\delta{jm}, but I don't seem to come up with any usefull answer. I...

"Proving" the Jacobi identity from invariance Hi all, In an informal and heuristic manner, I have heard that the "change" in something is the commutator with it, i.e. \delta A =[J,A] for an operator A where the change is due to the Lorentz transformation U = \exp{\epsilon J} = 1 + \epsilon J...

If we assume the inner product is linear in the second argument, the polarization identity reads (x,y) = \frac 14 \| x + y \|^2 - \frac 14 \| x - y \|^2 - \frac i4 \|x + iy\|^2 + \frac i4 \| x - iy \|^2. But there is another identity that I've seen referred to in some texts as the...

Homework Statement Prove that the identity map \mathrm{id}_{S^{2k+1}} and the antipodal map -\mathrm{id}_{S^{2k+1}} are smoothly homotopic. Homework Equations N/A The Attempt at a Solution My attempt: Fix k \in \mathbb{Z}_{\geq 0} and let \{e_i\}_{i=1}^{2k+2} be the standard basis for...

Homework Statement cos(x-y)cosy-sin(x-y)siny=cosx a.try to prove that the equation is an identity b. determine a counterexample to show that it is not an identity Homework Equations cos(x-y) = cosxcosy+sinxsiny sin(x-y) = sinxcosy-cosxsiny The Attempt at a Solution a.Left side of...

Homework Statement \frac{cos^{2}t+tan^{2}t -1}{sin^{2}t} = tan^{2}t Homework Equations Here are all the trig identities we know up to this point (the one's that we have learned so far, obviously we derive many others from these when verifying identities). Pythagorean Identities...

prove 1-(cos(x)+sin(x))(cos(x)-sin(x))=2sin^2(x) foil out the center I get 1-cos^2(x)-cos(x)sin(x)+cos(x)sin(x)+sin^2(x) the -cos(x)sin(x)+cos(x)sin(x) cancels to 0 leaving 1-cos^2(x)-sin^2(x) then I'm lost... I know I can switch 1-cos^2(x) to sin^2(x) but that doesn't help...

Could anyone please tell me how are those two expressions equivalent?! what are the identities used?

Show the following, where U is a vector, and r is the position vector: \nabla(U.r) = U in polar coordinates Many Thanks

When we talk about an abstract binary operation *:SxS --> S We say that an identity element "e" exists when e * x = x * e = x, (x; e belong to S) Now my questions: 1) If the operation is not commutative, does not this imply no identity? since e * x != x * e necessarily? 2) Does e * x...

Homework Statement (tan/(1-cot))+(cot/(1-tan))=1+(sec)(csc) The Attempt at a Solution This problem showed up in my class as a warm-up, and when my teacher tried to solve it for us he got stuck. I've asked a few classmates in higher level math, and they all seem to get stuck. I...

Hi there. I need help simplifying the following: |\sqrt{z^2 -1} +z| + |\sqrt{z^2 -1} -z| What I did was I rewrote z in polar coordinates, but I ran into some difficulties taking the square root of r^2(cos2θ-sin2θ)-1. I also tried rewritting z in exponential form, but also had problems. Help?

Homework Statement Let A be a square matrix such that I-A is nonsingular. Prove that A * (I-a)^-1 = (I-A)^-1 * A Homework Equations Now I think that A^-1 * A = A*A^-1 = I and I*A = A*I are relevant for this. The Attempt at a Solution I tried to express (I-a)^-1 in...

Homework Statement 1_R=identity in the ring R. /=...not equal Having some issues with this any help will be great: Let R be a ring with identity, such that x^2 = 1_R for all 0_R /= x ,where x belongs to R. How many elements are in R? Homework Equations The Attempt at a Solution...

Hey guys, I stumbled on an interesting and unexpected identity when looking for a simpler summation technique for inverse kinementics. Basically, I was trying to find a simpler way of summing IK vectors for some particular armature (like a tentacle or multi-branch armature on a robot). This...

Homework Statement I'm trying to write a proof ot demonstrate that every finite domain contains an identity element.Homework Equations The Attempt at a Solution If I can think of the operation from the ring as a mapping...like x->yx..where y are just values from the domain and then to consider...

How can I prove that every finite domain has an identity element? How should I think about the problem and what should I take into consideration?

On a set S with exactly one element x, define x + x = x, x*x = x. Prove that S is a ring. The way I think about this problem is be showing that it verifies certain axioms...like associativity,commutativity,identity,inverse for addition and commutativity for multiplication and a (b + c) = ab +...

dU = TdS - P dV Is in my book derived by viewing a proces of changing volume and energy in two separate steps. First you add energy with volume fixed, then change the volume. I'm just not sure that I understand why, you are allowed to do this. I know the changes are infinitesimal but why is...

1_R=identity in the ring R. /=...not equal Having some issues with this any help will be great: Let R be a ring with identity, such that x_2 = 1_R for all 0_R /= x ,where x belongs to R. How many elements are in R? Thanks

Homework Statement \alpha\frac{d}{d\alpha}[f(\alpha^ax,\alpha^by)]|_{\alpha=1}=ax\frac{\partial f}{\partial x}+by\frac{\partial f}{\partial y} Homework Equations The Attempt at a Solution Homework Statement I'm confused. I don't know what to do here. How to differentiate left...

I need to show that sin i*theta= i* sinh(theta). where sinh(theta) = .5[e^theta - e^(-theta)] and cos(theta) = .5[e^theta + e^(-theta)] and e^(i*theta) = cos(theta) + isin(theta) if I start with the formula sinh(theta) = .5[e^theta - e^(-theta)] and plug in e^(i*theta) = cos(theta) +...

Please I really need help with this homework question Prove without trig identity that f`(x)=0 for F(x)=Asin^2(Bx+C)+Acos^2(Bx+C)