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

In summary, the conversation is about proving an equation involving trigonometric identities. The equation to be proved is (x^2-1)(y^2-1)/xy + (y^2-1)(z^2-1)/yz + (z^2-1)(x^2-1)/zx = 4, given that xy+yz+zx=1. The conversation also mentions the importance of showing one's progress when seeking help on a math problem.
  • #1
skcollins
1
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
  • #2
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?
 

1. What are trigonometric identities?

Trigonometric identities are equations involving trigonometric functions that are true for all values of the variables within a certain domain. They are used to simplify and solve trigonometric equations.

2. How many types of trigonometric identities are there?

There are three main types of trigonometric identities: Pythagorean identities, quotient identities, and reciprocal identities. There are also double angle identities and sum and difference identities.

3. Why are trigonometric identities important?

Trigonometric identities are important because they allow us to manipulate and solve trigonometric equations more easily. They also have many applications in fields such as physics, engineering, and navigation.

4. How can I prove trigonometric identities?

There are several methods for proving trigonometric identities, including using algebraic manipulations, using geometric proofs, and using trigonometric identities themselves. Practice and familiarity with the identities is key to successfully proving them.

5. What are some common examples of trigonometric identities?

Some common examples of trigonometric identities include the Pythagorean identities, such as sin^2(x) + cos^2(x) = 1, and the double angle identities, such as sin(2x) = 2sin(x)cos(x). These identities are frequently used in trigonometry and calculus courses.

Similar threads

MHB Show x³y+y³z+z³x is a constant
    • General Math
Replies
1
Views
848
MHB Inequality in Triangle: Prove $|x^2+y^2+z^2-2(xy+yz+xz)|\le \frac{1}{27}$
    • General Math
Replies
1
Views
803
MHB Solving System of Equations: xy, yz, zx
    • General Math
Replies
3
Views
809
MHB What is the Sum of x, y, and z in a Non-Negative Real Number System?
    • General Math
Replies
4
Views
935
B Trigonometric Identity involving sin()+cos()
    • General Math
Replies
11
Views
1K
MHB Prove x²+y²+z² ≤ 2 For 0 ≤ x,y,z ≤ 1 with xy+yz+zx=1
    • General Math
Replies
6
Views
2K
MHB Prove Inequality for $x,y,z$ Positive Real Numbers
    • General Math
Replies
1
Views
1K
MHB Solve System of Equalities: x^2+xy+y^2, x^2+xz+z^2, y^2+yz+z^2
    • General Math
Replies
7
Views
734
MHB Prove Inequality: $x^2y\,+\,y^2z\,+\,z^2x \ge 2(x\,+\,y\,+\,z) - 3$
    • General Math
Replies
2
Views
1K
MHB Solve Algebra Challenge: $(x+1)(y+1)/(x+y)+\cdots
    • General Math
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top