identities Definition and 416 Threads

Homework Statement [/B]Q7 part a on one of the attached pictures 2. Homework Equations Trigonometric identities The Attempt at a Solution See attached pages Please help me I've spent onwards of 4 hours trying to figure this out and I can't get anywhere at all

I was supposed to simplify the expression ##\ln |\cot {x}|+\ln |\tan {x}\cos {x}|## and apparently it’s wrong. Where’s the mistake? Is it not simplified enough or . . . ? ##\ln |\cot {x}|+\ln |\tan {x}\cos {x}|## ##=\ln |\frac {\cos {x}}{\sin {x}}|+\ln |\frac {\sin {x}}{\cos {x}}\cdot \cos...

Homework Statement verify that theta in L = piD + (d-D)theta + 2Csin(theta) is equal to arc-cosine [(D-d)/2C] 2. The attempt at a solution you can see my attempt in the second picture uploaded. i don't think i even got it right

I have re-post this forum as I should have paid closer attention to rules. I apologized for that. Homework Statement 1) The expression tan^3 θ + sinθ/cosθ is equal to: (a) cot θ (b) tan θ sec^2 θ (c) tan θ (d) sin θ tan θ (e) tan θ csc^2 θ 2) Simplify (cos θ/1+ sin θ - cosθ/sinθ-1)^-1 (a)...

Please excuse my copying this question in, minimising my input :-) Part (b): Let $ a.b \times c =v $ Then $ a'.b' \times c' = \left( \frac{b \times c}{v}\right) . \left( \frac{c \times a}{v} \times \frac{a \times b}{v}\right) $ $ = v^{-1} \left(b \times c\right). \left[ \left(c \times...

If $$\cos(\pi/3)= \frac{1}{2}$$, find $$\sec(\pi-\pi/3)$$ Someone really give me step-by-step explanation. I really don't know what identity to use, and no idea how to get cosine to secant. Please, it would help. I do have more questions if you help me dissect this problem. XD Thanks so much in...

1) If $$\tan(\pi/4)=1$$, find $$\cot(\pi-\pi/4)$$. 2) If $$\cot(17^{\circ}) = 3.2709$$, find $$\tan(73^{\circ})$$ 3) If $$\cot(\theta) = \frac{-9}{2}$$ with $$\theta$$ in Quadrant II, find $$\sin (\theta)$$ --------------------------------------------- I really have no idea how to solve any...

1. Homework Statement I can't get the latex to render so I use ##\tilde a## to mean the slashed notation commonly seen in the Dirac equation, so ##\tilde a = \gamma^{\nu}a_{\nu}## which is also ##a_{\nu}\gamma^{\nu}## I think. Prove the following: ##\gamma^{\mu} \tilde{a} \gamma_{\mu} = -2...

Alright. I am sort of understanding this section on my online math lesson, but I am still struggling with it. Would be gladly appreciated if someone could help me with this: If cosΘ = -4/9 with Θ in Quadrant II, find sinΘ

Which of the following identities are true. Justify your answer. a)$n! = O(4^n)$ b)$4^n = O(n!)$ I have NO clue what to do here. First I was thinking let $n = 0$ so that $1 = O(1)$ (constant time complexity?)

[FONT=Century Gothic]If (sinΘ) = 2/3 with Θ in quadrant 1, find (secΘ) [FONT=Century Gothic]Θ = theta Completely new at trigonometric identities, would be a great help!

On page 51 Peskin and Schroeder are beginning to derive basic Fierz interchange relations using two-component right-handed spinors. They start by stating the trivial (but tedious) Pauli sigma identity...

Is there a way to simplify the proof of different vecot calculus identities, such as grad of f*g, which is expandable. And also curl of the curl of a field. Is there a more convenient way to go about proving these relations than to go through the long calculations of actually performing the curl...

Im to solve ##(k+l)^{2}e^{-ila}-(k-l)^{2}e^{ila}=0##, for ## k##, The solution is ##k=l(e^{ial}-1)/(e^{ial}+1)=il tan(al/2)## FIRST QUESTION So it's a quadratic in k, should be simple enough, my working so far using the quad. formula is ##k= (4l^{2}(e^{-ila}+e^{ila})\pm...

I would like to know how can I derive the double, half, product to sum, and sum to product identities of trigonometry using simple algebraic means. And which books (which I prefer) should I pickup at the library on this subject to actually learn these derivations? Or at the very least some...

Homework Statement [/B] Hi, I am currently working through a textbook, and the following simplification is given for an example question: I can't seem to work out how they have moved from cos(pi+n*pi) to cos(pi)cos(n*pi) so easily? Is there a simple trick I have missed? I understand the...

Dear All, I am studying electrodynamics and I am trying hard to clearly understand each and every formula. By "understand" I mean that I can "truly see its meaning in front of my eyes". Generally, I am not satisfied only by being able to prove or derive certain formula algebraically; I want to...

I'm completely lost here. I've got the cheat sheet of trig rules, but they don't appear to be helping me, I've watched a half dozen videos on each of cos sin and tan, and nearly all of them discuss the wrong topic. I don't want help on any single problem, but advice. How can I make sense of the...

Homework Statement Show that (sin^4 x + (sin^2 x * cos^2 x)) / (cos^2 x - 1) == -1 Homework Equations Sin^2 x + cos^2 x == 1 The Attempt at a Solution (sin ^4 x + (sin^2 x * cos^2 x)) / (cos^2 x - 1) = ((sin^2 x)(sin^2 x) + (sin^2 x * cos^2 x)) / (cos^2 x - 1) =((sin^2 x)(1 - cos^2 x) +...

1) Question statement: Simplify 2sec^2x-2sec^2xsin^2x-sin^2x-cos^2x 2)Relevant equations: tan A=sinA/cos A 1+tan^2A=sec^A cot A=1/tanA cot A=cos A/sinA sin^2A+cos^2A=1 secA=1/cos A cosecA=1/sinA 1+cosec^2A= cot^2A sin2A=2sinAcosA cos2A=1-2sin^2A=cos^2A-sin^2A=2cos^A-1 tan2A=(2tanA)/1-tan^2A 3)...

1) Problem statement: Solve the trigonometric equation for the domain is. 0°<x<360° 5(sinx - cosx) = 4sinx - 3cosx 2) Relevent equations: secx=1/cosx cosec x=1/sinx cot x= 1/tanx tan x=sinx/cosx cot x=cosx/sinx sin^2 x + cos^2 x=1 1 + tan^2 x= sec^2 x 1+ cot^2 x = cosec^2 x Template of answer...

Homework Statement By using a suitable vector identity for ∇ × (φA), where φ(r) is a scalar field and A(r) is a vector field, show that ∇ × (φ∇φ) = 0, where φ(r) is any scalar field. Homework Equations ∇×(φA) = (∇φ)×A+φ(∇×A)? The Attempt at a Solution I honestly have no idea how to even...

Transform the left hand member into the right hand member. $\frac{\tan\alpha+\tan\beta}{\sec\alpha-\sec\beta}=\frac{\sec\alpha+\sec\beta}{\tan\alpha-\tan\beta}$By using cross multiplication I was able to prove this identity but what I actually want to accomplush is to transform the left member...

I already did everything that I can to transform the left side member to the right side member but I always get a jumbled terms. Please give me a hand on this problem. $(2\sin^{2}(\theta)-\cos^{2}(\theta))^{2}-9(2\sin^{2}(\theta)-1)^{2}=(2-3\sin^{2}(\theta))(2+3\sin(\theta))(3\sin(\theta)-2)$

Transform the left member to the right member. $\frac{\left(\sin^{2}(\phi)\cos^{2}(\phi)+\cos^{4}(\phi)+2\cos^{2}(\phi)+\sin^{2}(\phi)\right)}{1-\tan^{2}(\phi)}=\frac{3+\tan^{2}(\phi)}{1-\tan^{4}(\phi)}$ I begin by regrouping the numerator of the left...

Hey all! I am having some trouble with a certain problem on my homework. I would like some guidance. I have to prove one side of the equation is equal to the other, as you may know, as this is an algebraic proof. This in itself isn't too hard. The hard part is just this one particular problem. I...

Help me get started with these problems. Prove the following$\frac{\tan(A)}{1-\cot(A)}+\frac{\cot(A)}{1-\tan(A)}=\sec(A)\csc(A)+1$ $\frac{\sec(A)-\tan(A)}{\sec(A)+\tan(A)}=1-2\sec(A)\tan(A)+2\tan^{2}(A)$

Hey guys, I'm about to finish answering the chapter problems on my trigonometry books about proving Identities, there are 2 problems that made me scratch my head though. They are the last 2 problems left that I'm not yet able to verify. I would greatly appreciate it if you could lend me some...

Again I'm stuck with another problem in proving identities. This is the 46th item in the list of 53 identities that I'm asked to verify and so far I was able to prove 45 of them, there are 8 items left and one of them is this Identity $\cos^{6}(A)+\sin^{6}(A)=1-3\sin^{2}(A)\cos^{2}(A)$ Thanks!

Hey guys, I'm just going over my work files for this week and I've noticed 2 problems that have fooled me, and seem a little bizarre for my current mathematical level. They do involve trig, and a part of me is hoping for a misprint on the sheet, but I'm more sure that it's my own inadequacies...

Hi! (Wave) Let $R$ be a relation. Show the following sentences: $dom(R^{-1})=rng(R)$ $rng(R^{-1})=dom(R)$ $fld(R^{-1})=fld(R)$ $(R^{-1})^{-1}=R$ That's what I have tried: Let $x \in dom(R^{-1})$. Then $\exists y$ such that $<x,y> \in R^{-1} \Rightarrow <y,x> \in R \Rightarrow x \in...

hi deoes anyone know any online resource for proofs of Dirac delta function identities and confirming which representations are indeed DD functions Thanks a lot.

Hey guys, I've been trying to wrap my mind around this problem but I've really come up short. Any help would be amazing. If tanX=10 Find the exact value of cot(pi/2 - x)

Homework Statement div(øu) = ødivu + ugradø Homework Equations divergence of scalar field = f,ii divergence of vector field = ui,i The Attempt at a Solution I've heard this is a simple proof, but this is my first one of 8 or so proofs I need to complete for homework, and I'm...

is there an equivalent identity for $\sin^2\omega t?$ please tell me.REGARDS!

Homework Statement I'm trying to simplify some trigonometric expressions, I'm attaching my work here. This comes from a famous physics problem i.e. the rod with two masses spinning on a circle. I've tried many times but I just can't get it. Any help on which identities to use would really...

Hey, so today for our quantum physics class we were supposed to go through these identities, |+_x > = \frac{1}{2^{0.5}} (|+> + |->)|-_x > = \frac{1}{2^{0.5}} (|+> - |->) |+_y > = \frac{1}{2^{0.5}} (|+> + i|->) |-_y > = \frac{1}{2^{0.5}} (|+> - i|->)where |+ (x)> would represent spin up...

Proving identities is a pain! Thanks in advance, guys! Homework Statement 1. 1 + sec^(2)xsin^(2)x = sec^(2)x 2. sinx/1-cosx + sinx/1+cosx = 2cscxHomework Equations The Attempt at a Solution For the first problem, this is the best I got: 1 + sec^(2)x(1-cos(2)x) For the second problem, I...

Homework Statement Factorate the expression a(1-b²)(1-c²) + b(1-c²)(1-a²) + c(1-a²)(1-b²) - 4abc Homework Equations Algebric identities The Attempt at a Solution It seems to be an olympic problem, and I can't find the right factors for it. I would really appreciate the help and, if...

[SIZE="4"]Definition/Summary In a right-angled triangle, with a hypotenuse ("hyp"), and with sides adjacent ("adj") and opposite ("opp") to the acute angle we are interested in, the six basic functions are defined as follows: sin = opp/hyp, cos = adj/hyp, tan = opp/adj, cosec = 1/sin, sec...

The definition I have for a 2-point correlator is $$\langle \phi_1(x_1)\phi_2(x_2)\rangle = \frac{1}{Z} \int \mathcal D \phi \,\,\phi_1(x_1)\phi_2(x_2) \exp-S[\phi],$$ where ##Z = \int \mathcal D \phi \,\,\exp-S[\phi]##. I am trying to understand the overall physical meaning of such a quantity...

Homework Statement In integration, we are allowed to use identities such as sinx = \sqrt{1-cos^2x}. Why does that work, and why doesn't make a difference in integration? Graphing \sqrt{1-cos^2x} is only equal to sinx on certain intervals such as(0, \pi) and (2\pi, 3\pi). More correctly...

In integration, we are allowed to use identities such as $$sinx = \sqrt{1-cos^2x}$$. Why does that work, and why doesn't make a difference in integration? Graphing $$\sqrt{1-cos^2x}$$ is only equal to sinx on certain intervals such as$$ (0, \pi) $$and $$(2\pi, 3\pi)$$. More correctly, shouldn't...

prove the following identities $\cos(2\theta)=\cos^{2}(\theta)-\sin^{2}(\theta)$ $\sin(2\theta)=2\cos(\theta)\sin(\theta)$our Demoivre's formula says $z=r\left(\cos(\theta)+i\sin(\theta)\right)$ I don't know how use it to prove the identities above please help me get started. regards!

I'm trying to explicitly show that \varepsilon^{0 i j k} \varepsilon_{0 i j l} = - 2 \delta^k_l I sort of went off the deep end and tried to express everything instead of using snazzy tricks and ended up with \begin{eqnarray*} \delta^{\mu \rho}_{\nu \sigma} & = & \delta^{\mu}_{\nu}...

Please forgive me as I may have to edit this post to get the equations to show properly. I am doing some work with AC circuits and part of one of my phasor equations has this in it: \frac {2i} {1+cos(θ) + i sin(θ)} - i , where i is the imaginary number \sqrt{-1}. However, knowing the...

Homework Statement The length of the curve r(t) = cos^3(t)j+sin^3(t)k, 0 =< t <= pi/2 is Homework Equations AL in polar = ∫sqrt(r^2 + [dr/dθ]^2) The Attempt at a Solution I am having trouble simplifying the terms within the square root. What method should I use to deal with...

6b) tanh^2(x) + 1/cosh^2(x) = 1 Could someone help start me off? I know that you have to sub in (e^x + e^-x)/2 for cosh and (e^x - e ^-x)/(e^x + e ^-x) for tanh. Then I'd add these together, but I'm not sure how I'd solve/simplify them arithmetically after that. Help would be appreciated! thanks.

About the Newton's identities: I'm right if I state that ek = Ik, pk = tr(Ak) and hk = det(Ak) (being Ik the kth-invariant of the matrix A)?

Look this relationship: http://en.wikipedia.org/wiki/Newton%27s_identities#Related_identities If I isolate the variable p, I'll have: ##p_1 = 1h_1## ##p_2 = 2h_2-h_1p_1## ##p_3 = 3h_3-h_2p_1-h_1p_2## So, my question is: BTW, would be true that: ##p_1 = 1h_1## ##p_2 = 2h_2+h_1p_1## ##p_3 =...