identities Definition and 416 Threads

Homework Statement Prove the following vector identity: \nablax(AxB) = (B.\nabla)A - (A.\nabla)B + A(\nabla.B) - B(\nabla.A) Where A and B are vector fields. Homework Equations Curl, divergence, gradient The Attempt at a Solution I think I know how to do this: I have to...

Homework Statement Prove (using the left side): sinΘ tanΘ = cosΘ sec^2Θ - cosΘ Homework Equations The Attempt at a Solution

I want to verify my understand of this. Let u defined in region \Omega with boundary \Gamma. If u = 0 \hbox { on the boundary } \Gamma, then u = 0 \hbox { in the region } \Omega. The way to look at this, suppose u is function of x component called Xand y component called Y. So...

Homework Statement Suppose u is harmonic (\nabla^2 u = 0 ) and v=0 \;\hbox{ on } \;\Gamma where \Gamma is the boundary of a simple or multiply connected region and \Omega is the region bounded by \Gamma. Using Green's identities, show: \int \int_{\Omega} \nabla u \cdot \nabla v \...

This is to solve Dirichlet problem using Green's identities. The book gave some examples. My question is: Why the book keep talking v is harmonic(periodic) function. What is the difference whether v is harmonic function or not as long as v has continuous first and second derivatives...

Homework Statement Left Inversion in Rectangular Cases. Let A^{-1}_{left} = (A^{T}A)^{-1}A^{T} show A^{-1}_{left}A = I. This matrix is called the left-inverse of A and it can be shown that if A \in R^{m x n} such that A has a pivot in every column then the left inverse exists. Right...

I have always been curious as to where the definition of cosh(x) and sinh(x) come from and how they are related to the natural exponential. I know it has something to do with Euler's formula but I don't know the details of the derivation. Could anyone shed some light on this? I haven't yet...

Homework Statement Left Inversion in Rectangular Cases. Let A^{-1}_{left} = (A^{T}A)^{-1}A^{T} show A^{-1}_{left}A = I. This matrix is called the left-inverse of A and it can be shown that if A \in R^{m x n} such that A has a pivot in every column then the left inverse exists. Right...

Homework Statement sin^3(x)-cos^3(x) sin(x) - cos(x) equals 1 + sin(x) + cos(x) Homework Equations Not sure :/ The Attempt at a Solution Not sure where to even start.

Given sinθ = 0.6, calculate tanθ without using the inverse sine function, but instead by using one or more trigonometric identities. You will find two possible values. I found one of the values using sin^2 (theta) + cos^2 (theta) = 1 I tried using cos (90 + theta)= sin theta to find the...

Homework Statement Can you conclude that A = B if A, B, and C are sets such that A \cup C = B \cup C and A \cap C = B \cap C Homework Equations The above is part c of a problem. The problems a and b are as follows A) A \cup C = B \cup C My answer: I gave a counter example...

Homework Statement Show that in 2 dimensions a skew-symmetric tensor of second rank is a pseudoscalar and that one of third rank is impossible. The Attempt at a Solution A11=A22=0, while A12=-A21, which makes A= A12+A21, which is certainly skew-symmetric, though I am not sure it is...

Homework Statement 1. Establish the vector identity \nabla . (B x A) = (\nabla x A).B - A.(\nabla x B) 2. Calculate the partial derivative with respect to x_{k} of the quadratic form A_{rs}x_{r}x_{s} with the A_{rs} all constant, i.e. calculate A_{rs}x_{r}x_{s,k} Homework Equations The...

[b]1. How do I prove sinxcosxsec^2x=tanx Homework Equations sec^2x = tan^2x + 1 The Attempt at a Solution sinxcosx(tan^2x + 1) tan^2xsinxcosx +sinxcosx sin^2x/cos^2x*sinxcosx + sinxcosx - is this valid? I'm not sure what I've done is even correct - but it doesn't seem...

These identities might be considered as true: \begin{array}{rcl} 1 - 1 + 1 - 1 + \cdots & = & \frac{1}{2} \\ 1 - 2 + 3 - 4 + \cdots & = & \frac{1}{4} \\ 1 - 4 + 9 - 16 + \cdots & = & 0 \\ 1 + 1 + 1 + 1 + \cdots & = & -\frac{1}{2} \\ 1 + 2 + 3 + 4 + \cdots & = & -\frac{1}{12} \\...

Homework Statement Show that v\nablav = \nablaxvxv v · ∇v = ∇(0.5v2 + c × v c=∇ × v My attempt ∇(A · B)= B · ∇A + A · ∇B + B×(∇×A) + A×(∇×B) Replace A and B with V ∇(v · v)= v · ∇v + v · ∇v + v×(∇×v) + v×(∇×v) v · ∇v = ∇(0.5v2 - v×(∇×v) Is v×(∇×v) = =∇ × v × v? And...

Homework Statement 1/cscx-sinx = secx tanx Homework Equations cscx = 1/sinx secx = 1/cosx The Attempt at a Solution 1/cscx-sinx = secx tanx L.S. = 1/cscx-sinx = 1/(1/sinx)-sinx R.S. = secx tanx = (1/cosx)(sinx/cosx) This is where I'm getting confused. Why can't...

1. sec^4 x + sec^2 x tan^2 x - 2 tan^4 x = ? The possible answers are: a. 4 sec^2 x b. 3 sec^2 x - 2 c. sec^2 x + 2 d. tan^2 x - 1 Homework Equations No idea. The Attempt at a Solution I'm not sure where to begin here. My book first doesn't cover anything above...

Homework Statement How to get from \sqrt{2+2cosx} to 2cos(x/2) The Attempt at a Solution I'm pretty much stuck on this. I can only see that is simplifies by taking out the common factor 2, which isn't correct.

Homework Statement Verify that each equation is an identity- directions Problem- csc(A-B)=secB ---------------- <<< divide bar sinA-cosAtanB Homework Equations well i tried to put in terms of sin cos and I've gotten stuck The...

Homework Statement Prove the vector identity: \left(a\times\nabla\right)\bullet\left(u \times v\right)=\left(a \bullet u \right)\left(\nabla \bullet v \right)+\left(v \bullet \nabla \right)\left(a \bullet u \right)-\left(a \bullet v \right)\left(\nabla \bullet u \right)-\left(u...

Homework Statement 1. cos θ - 1 / cos θ = sec θ - sec^2 θ 2. (sin θ + cos θ)^2 = 1 + 2 sin θ cos θ 3. (1 / 1 + cos θ) + (1 / 1 - cos θ) = 2csc^2θ Homework Equations 1 / cos θ = sec θ 1 / sin θ = csc θ sin^2 θ + cos^2 θ = 1 cos^2 θ = 1 - sin^2 θ sin^2 θ = 1 - cos^2 θ...

cos(x-(pie/2))=cos(x)tan(x) I have to verify this identity and can't seem to figure it out. cos (x-y)=cos x * cos y + sin x * sin y well since cos y = 0, it kind of eliminates that side of the equation and I end up with sinx * sin1 Did I go about this all wrong?

Homework Statement Prove Trig. Identities 1. sec θ (sec θ - cos θ)= tan^2 θ Homework Equations sec θ = 1/cos θ tan θ = sin θ/ cos θ cot θ = cos θ / sin θ The Attempt at a Solution 1. sec θ * sec θ - sec θ * cos θ 1/ cos θ * 1/ cos θ - 1/ cos θ * cos θ ----> cos θ is...

Homework Statement Cos^2x-Sin^2x/2 SinxCosx The Attempt at a Solution I changed cos^2x to 1- sin^2x which then the equation was 1- s sin^2x/2snxcosx and i have no idea how to make this a single trig. function

Homework Statement This is actually many steps through a calculus problem involving trig functions. I have not included the problem because I'm trying very hard to figure it out on my own (at least as far as it's possible). I've found the answer I'm looking for, but it's attached to a bunch...

cos = sin (pi/2-theta)

Homework Statement Without using tables(calculators) find the numerical value of Sin[Pi/8]^2 - Cos[3 (Pi/8)]^4 Homework Equations The Attempt at a Solution I tried changing it to: 1-cos[pi/8]^2 - cos[3pi/8]^4 but have no idea where to go... its really got me scratching my...

Homework Statement (Give a combinatorial proof of each of the following identities. In other words, describe a collection of combinatorial objects and then explain two different methods for counting those objects. Leave each identity in the form given. Do not rearrange terms or use any other...

Homework Statement 3sinx = 1 + cos 2x Homework Equations N/A The Attempt at a Solution 3sinx = 1+1 - 2sin2x (Trigonometric Identity) 3sinx = 2-2sin2x 2sin2x + 3sinx = 2 I do not know where to go from there. My book tells me the answer is 30o and 150o

Homework Statement 12cot2(2x)=4 (8 exact answers) 3cos2(3x)=2sin(3x) (6 decimal answers) cos(3x)=sec(3x)+2tan2(3x) (6 exact answers) hint(get all cosines) <- teacher wrote that And then I have to prove by working on one side: sin3(x) / 1-cosx = sinx*cosx+sinx and (sinx / cosx-1) + (sinx /...

Homework Statement (sin3+cos3)/(sin+cos) Homework Equations sin2+cos2=1 1 +cot2=csc2 1+tan2=sec2 Are these sufficient? The Attempt at a Solution Confusion. Epic confusion. I might have had it yesterday, but the mathematical equivalent of a writers anti-tank roadblock. At best...

How do I prove that (1+sin2x) = (cosx) (cosx + sinx) (cosx - sinx)

Can someone please help me with these two questions. Th first one is prove: 1-tan^2x ________ = cos2x 1+tan^2x & the second one is prove: sinx+ sinxcot^2 = secx

The question asks you to simplify sin(3pi/2+x). I know that you've got to use the sin(a+b)=sinacosb+cosasinb but I'm not sure how to solve it when it's not a special triangle. Any help is much appreciated.

Homework Statement For arbitrary vector fields A and B show that: ∇.(A ∧ B) = B.(∇∧A) - A.(∇∧B) The Attempt at a Solution I considered only the 'i'-axis, by saying that it is perpendicular with A and B and then I expanded both the left and right side out. The working is...

I have been trying to do this problem for a long time, and still can not do it. I know the answer is sin2x, but I have no idea how to do it: write expression as sine, cosine, or tangent of an angle sin3xcosx - cos3xsinx THANKS!

Ok guys, here's my problem. I left on vacation with my parents before I learned how to do these correctly. I have been trying and I sort of have the gist of them down. For instance, tan A*sec A simplified is sin A. A=theta. But as I move on they stop making sense, and this is where my problem...

hello. i have a question about trignometric identities.. it's realtivly easy, but am struggling with the algebra in it ( Algebra + trig = Very confusing to me ) Prove that .. [Sinx/(1+Cosx)] + [(1+cosx) / sinx] = 2csc x i manged to get it to [Sin2x+1+2cosx+cos2x] / SinxCosx...

Homework Statement Okay, so this is some trig I learned last year but have since forgotten. If you can give me the first step, I can solve the rest on my own. The given statement is true and you have to prove why using Pythagorean Identities. csc2\alpha-1 = cos2\alpha ________ csc2\alpha

In QED, the Ward identities set Z_1=Z_2 and Z_1 - 1 = \left. {\frac{{d\Sigma \left( p \right)}}{{dp}}} \right|_{p = m} . This can be shown explicitly for the 1-loop calculations if one uses an on-shell subtraction scheme, where the renormalized mass and charge are identical to the...

Homework Statement By using trig formulas show that, sin(2x + pi/3) = sin(2x) + sin(2(x+pi/3)) Homework Equations Trig Identities The Attempt at a Solution I've used double angle formulas, sin(a+b) formulas, I just can't seem to get it.

Homework Statement Can anyone here help me find how and where trig identities are used in real life. can you also tell me which identity(with example) and is used for what purpose and how. Homework Equations The Attempt at a Solution I found out that it is used in the field...

Homework Statement for homework we have to find 2 different dirrivatives of the same problem (one may be incorrect) and then tell if they are equal 2. The attempt at a solution original y=sec(x)*cot(x) the two derrivatives (i know these are correct becase i have compared with others in...

Homework Statement Prove that this is an identity. 1 + cos² x / sin² x = 2csc² - 1 Homework Equations cos²x + sin²x = 1 (manipulative equation) tan²x = sec² - 1 cot²x = csc²x - 1 etc.. The Attempt at a Solution I attempted this equation more than 10+ times. Each time, I find a...

Homework Statement 2x^2 + 7x - 5 = A(x-1)^2 + Bx + C Homework Equations N/a The Attempt at a Solution This is an interesting equation as regardless of the whether I substitute x = 0 or x = 1 i still encounter the problem of not be able to make the calculation any easier. I...

Homework Statement By substituting y for 9x^2 solve 81x^4 - 63x^2 + 10 = 0 Homework Equations The Attempt at a Solution My attempt at a solution is: y^2 - 7y + 10 (y-2)(y-5) therefore y = 2 y = 5 Can someone double check this? Cheers

Homework Statement Prove that \frac{sin3x}{sinx}-\frac{cos3x}{cosx} = 2Homework Equations The Attempt at a Solution LHS:\frac{sin(2x+x)}{sin}-\frac{cos(2x+x)}{cosx} =\frac{sin2x.cosx + cos2x.sinx}{sin}-\frac{cos2xcosx - sin2x.sinx}{cosx}

Hi guys, sry if i asked a silly qns. Is the below equivalent is true?

Homework Statement Show that (sin(2theta) - sin(theta)) / (cos(2theta) - cos(theta) + 1) = tan(theta) sorry if this setting out is unclear but i am not familiar with how to post math symbols and such. Homework Equations above The Attempt at a Solution I have tried simplifying...