MHB How to Prove a Trigonometric Identity Involving x, y, and z?

skcollins
Messages
1
Reaction score
0
If xy+yz+zx=1 then prove (x^2-1)(y^2-1)/xy+(y^2-1)(z^2-1)/yz+(z^2-1)(x^2-1)/zx=4 with trigonometric identities such as cotAcotB+cotBcotC+cotCcotA=1
 
Mathematics news on Phys.org
Hello skcollins and welcome to MHB! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Thread 'Useless continued fraction for 1'

I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
View full post »

Similar threads

MHB Show x³y+y³z+z³x is a constant
Replies
1
Views
1K
MHB Solving System of Equations: xy, yz, zx
Replies
3
Views
1K
MHB Prove x²+y²+z² ≤ 2 For 0 ≤ x,y,z ≤ 1 with xy+yz+zx=1
Replies
6
Views
2K
MHB Prove Inequality for $x,y,z$ Positive Real Numbers
Replies
1
Views
1K
MHB What is the Sum of x, y, and z in a Non-Negative Real Number System?
Replies
4
Views
1K
MHB Prove Inequality: $x^2y\,+\,y^2z\,+\,z^2x \ge 2(x\,+\,y\,+\,z) - 3$
Replies
2
Views
1K
B Trigonometric Identity involving sin()+cos()
Replies
11
Views
2K
MHB Find Min of $\frac{a(x^2+y^2+z^2)+9xyz}{xy+yz+zx}$ for $x+y+z=1$
Replies
4
Views
2K
MHB Solve Algebra Challenge: $(x+1)(y+1)/(x+y)+\cdots
Replies
3
Views
2K
MHB Solve System of Equalities: x^2+xy+y^2, x^2+xz+z^2, y^2+yz+z^2
Replies
7
Views
1K

Hot Threads

Recent Insights

Back
Top