Proving a Sinh(x) expression to be an integer

  • Thread starter Thread starter supersticky99
  • Start date Start date
  • Tags Tags
    Expression Integer
Click For Summary
SUMMARY

The discussion centers on proving that sinh²(ln(√2 + √3)) equals 2. A participant confirmed this result using a calculator but sought a proof without computational tools. The approach involved rewriting sinh² using the identity (1/4)(e²x + e⁻²x - 2) and applying logarithmic properties. The next step suggested was to utilize the identity exp(ln(x)) = x to simplify the expression further.

PREREQUISITES
  • Understanding of hyperbolic functions, specifically sinh²
  • Familiarity with logarithmic identities and properties
  • Basic knowledge of exponential functions and their inverses
  • Proficiency in algebraic manipulation of expressions
NEXT STEPS
  • Study hyperbolic function identities and their applications
  • Learn advanced logarithmic manipulation techniques
  • Explore proofs involving exponential functions and their properties
  • Investigate the relationship between logarithms and hyperbolic functions
USEFUL FOR

Mathematicians, students studying advanced calculus, and anyone interested in the properties of hyperbolic functions and logarithmic proofs.

supersticky99
Messages
1
Reaction score
0
Prove or disprove: sinh2(ln([tex]\sqrt{}2[/tex]+[tex]\sqrt{}3[/tex])) is an integerObviously, I used my calc to figure out that the answer is 2. Proving it w/o a calc is hard though.

The Attempt at a Solution



I've tried rewriting sinh2 as (1/4)(e2x+e-2x-2) and after all the substitutions and log rules I get (1/4)(ln([tex]\sqrt{}2[/tex]+[tex]\sqrt{}3[/tex])+1/(ln([tex]\sqrt{}2[/tex]+[tex]\sqrt{}3[/tex]))-2)

what now?...
 
Physics news on Phys.org
Use the identity

[tex] \exp{(\ln{x})}=x[/tex]

to eliminate exp and ln.

ehild
 

Similar threads

Solve the given trigonometry equation
  • · Replies 7 ·
Replies
7
Views
1K
Prove that the integral is equal to ##\pi^2/8##
  • · Replies 105 ·
4
Replies
105
Views
11K
Shine Bright: Solving the Equation \sinh 3x = 4\sinh^3x + 3 \sinh x
  • · Replies 5 ·
Replies
5
Views
2K
Special Comparison Test For Infinite Series
  • · Replies 4 ·
Replies
4
Views
2K
Solve the differential equation: y′′y′+yy′+yy′′=0
  • · Replies 5 ·
Replies
5
Views
2K
Proving that ##\lim [\sqrt{4n^2 +n} - 2n] = \frac{1}{4}##
  • · Replies 9 ·
Replies
9
Views
3K
Calculating Area Under a Curve Using Change of Variables and Quotient Rule
  • · Replies 5 ·
Replies
5
Views
2K
Proving function f(x) is a PDf given integral relationships
  • · Replies 1 ·
Replies
1
Views
2K
Solving Multivariate Problem: Critical Points for ##y=-x##
  • · Replies 2 ·
Replies
2
Views
2K
Solving hyperbolic trigonometric equations
  • · Replies 1 ·
Replies
1
Views
1K