# identity

1. ### Proving a vector identity Cartesianally

I have undergone several proofs to my question which is: Show that div(F*G) = G . curl F - F . curl G Attached album via imgur: /7 - Album on Imgur The attached album to which I have uploaded my work on imgur shows my question and the seven solutions I have done (and had help with from...
2. ### vector identity proof

Hi all, this is my first post here :) Nice forum by the look of things. Anyway my teacher showed me this I will attach the link here: It is page 2 from this link: http://www2.ph.ed.ac.uk/~mevans/mp2h/VTF/lecture15.pdf At 15.3. the pdf discusses: Products of Two Vector Fields: When...
3. ### Algebraic identity

Prove that: \sqrt{2}\sqrt{1-\sqrt{1-x^2}}=\vert\sqrt{1+x}-\sqrt{1-x}\vert
4. ### Kronecker product identity

Hi, during my exploration of some matrix operations I came to a suspicion that following itentity holds (A,B are square matrices both with n rows and n columns and \otimes is so called Kronecker product): det(A\otimes B-B\otimes A)=0 Do you know a proof of this fact? (I have tried to use this...
5. ### Trig substitution (the disappearing identity)

I thought I was finally getting the hang of this. Finally seeing what's happening then tan theta disappears. What just happened with this expression beyond the the red arrow spot
6. ### sine/cosine sum identity

Does anyone know of a proof for the sine and cosine sum identities, sin(a+b)=sin(a)cos(b)+cos(a)sin(b) sin(a-b)=sin(a)cos(b)-cos(a)sin(b) cos(a+b)=cos(a)cos(b)-sin(a)sin(b) cos(a-b)=cos(a)cos(b)+sin(a)sin(b) that doesn't involve using the diagram in the link...
7. ### a horrible looking trigonometric identity

I am really stuck in the identity below. Prove \frac{\cos A + \cos(120^\circ + B) + \cos(120^\circ - B)}{\sin B + \sin(120^\circ + A) - \sin(120^\circ - A)} = \tan\frac{A + B}{2} Using sums and differences, I can simplify the terms with {120^\circ} \cos(120^\circ + B) + \cos(120^\circ -...
8. ### Identity with binomial coefficients

I have to show that \sum \limits_{n=m}^\infty \binom{n}{m} x^{n-m} = \frac{1}{(1-x)^{m+1}} for m \geq 0 and \forall x \in \mathbb{C} with \|x\| <1 . If I compute the left side I get \sum \limits_{n=m}^\infty \binom{n}{m} x^{n-m} =...
9. ### Does this semigroup have an identity?

Let G be the set of functions that map {1,2,3,4} into {1,2}, the binary operation is the usual composition of mappings and G is a semigroup. From my knowledge, I would say that it doesn't have an identity since it would need to be f(x)=x where x is an element of {1,2,3,4}. But f(x)=x maps...
10. ### Trig Identity Question

Hi there! If someone could solve the following question WITH justification in the brackets beside each step e.g. 1/cosx = secx I would really appreciate it! Question: [(1-cos2x + sin2x)/(1+cos2x + sin2x)] = tanx P.S. The more the steps the better.
11. ### Help with Euler's identity; i = 0??

- e^(i2Ï€) = 1 - e^(i2Ï€) = e^0 - i2Ï€ = 0 - i = 0 (?) Where is the mistake?
12. ### Working with an affine transformation of the identity matrix

Hi, I'm working with matrices of the form M = a I + b, where I is an nxn identity matrix and a, b are scalars. In particular I need to invert matrices of this form, for general n. It appears as though these inverses have a very simple form, but I can't characterize this form general...
13. ### Trigonometry Identity.

How to prove this identity? \frac{\cos 2\alpha+\cos 2\beta}{1+\cos 2(\alpha+\beta)}=\frac{\cos (\alpha-\beta)}{\cos (\alpha+\beta)} I've tried solving from L.H.S and R.H.S. But failed. Can anyone guide me? Thanks.
14. ### Zeta function identity

Probably something like this has been proven before, but I have derived the following: $\zeta(s) = \displaystyle\frac {7} {4} -\sum\limits_{a=2}^\infty \sum\limits_{b=2}^\infty \frac{1} {a^{bs}-1}$ I tried checking to make sure that it works by letting $s=1$, but then the RHS appears to either...
15. ### Help! - trig identity

How do I solve secx/(cotx+tanx)=sinx by only working with the left side?
16. ### Prove gamma function's trig identity?

I am interested in the process and a specific example behind deriving that gamma(x)*gamma(1-x)=pi*csc(pix). The proof or derivation doesn't seem to exist anywhere online.
17. ### Eulers Identity: e^(i*pi) = -1 vs bellCurve: sqrt( e^(i*x)^(i*x) / circle ) ?

Eulers identity: e^(i*pi) = -1 Bell curve: e^(-x*x/2)/sqrt(2*pi) (x^y)^z = (x^z)^y = x^(y*z) e^(-x*x/2) = sqrt( e^(-x*x) ) = sqrt( e^((i*x)*(i*x)) ) = sqrt( (e^(i*x))^(i*x) ) Divide by circumference of a circle (which I left off to simplify until now): bell curve height = sqrt(...
18. ### Trigo identity

How do I solve this: tg(0.5arctgx)? I know that tg(arctgx)=x, but I don't know what to do when I also have a number inside the brackets...
19. ### Trigonometric identity

Hello, I need to find a trigonometric identity that connects between arctg(x) and arccot(x). I know that arccos(x) and arcsin(x) have this identity: arccos(x)+arcsin(x)=pie\2 Is there identity like that for arctg(x) and arccot(x)?
20. ### Questions about trig identity statements

I have two questions: 1. How does 3\cos ^{2}(x) - 2\sin^2(x) = 3 - 5\sin^{2}(x) and 2. How does \cos^3(x) - 2\cos(x)(1 - \cos^2(x)) = 3\cos^3(x) - 2\cos(x).