The discussion revolves around evaluating the limit of the expression (1 + cos(2x)) / cos(3x) as x approaches π/2. The subject area involves trigonometric limits and identities.
The discussion is ongoing, with participants offering different perspectives on the limit evaluation process. Some have proposed specific substitutions and transformations, while others have pointed out potential flaws in reasoning. There is a recognition of the need to clarify certain steps and assumptions, but no consensus has been reached.
Participants are working under the constraints of standard trigonometric identities and limits, and there is an acknowledgment of potential arithmetic errors in the calculations presented.
Dell said:the best i could come up with is
lim
x->pi/2 (1+cos2x)/cos3x
lim
x->0 2cos^2(pi/2-x)/cos(3(pi/2-2))
lim
x->0 (2sin^2(x))/sin(3x)
lim
x->0 2sin(x)*1/3
=0
lanedance said:With last comment in mind, I'm trying to pick the flaw in you logic... i think you miss a negative when you subsitute x->pi/2-x, and can't just cancel the (2sin^2(x))/sin(3x) to 2sin(x)*1/3.
This is beacasue of the trig identities allow you to write sin^2x as sin2x and so on, think what thismeans in terms of the taylor series...
in the mean time its worth trying Dick's suggestion though...