cos cos &#x2061;<!-- ⁡ --> (

ntaraxq 2022-07-06 Answered
cos cos ( A π ) where A is an irrational algebraic number
You can still ask an expert for help

Want to know more about Irrational numbers?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Pranav Greer
Answered 2022-07-07 Author has 13 answers
Let A be algebraic irrational. We claim that cos ( A π ) transcendental. Assume not: cos ( A π ) is algebraic. Then sin ( A π ) = ± 1 cos 2 ( A π ) is algebraic. Then e i A π = cos ( A π ) + i sin ( A π ) is algebraic. Also e i A π 0 and e i A π 1. Now 2 / A is algebraic irrational. Note
( e i A π ) ( 2 / A ) = e 2 π i = 1
is algebraic. This contradicts Gelfond-Schneider.
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more