SOLUTION: Show that the value of tan 3 α cot α cannot lie between 1/3and 3?

Algebra ->  Trigonometry-basics -> SOLUTION: Show that the value of tan 3 α cot α cannot lie between 1/3and 3?      Log On


   

Question 748654: Show that the value of tan 3 α cot α cannot lie between 1/3and 3?
Answer by AnlytcPhil(1810) About Me  (Show Source):
You can put this solution on YOUR website!
tan3α·cotα;

It's easy if you're taking calculus, and can use
L'Hopital's rule, but not if you aren't.  Tell me 
in the thank-you note form if you are taking 
calculus or just taking trigonometry.  Then I'll
help you with it.  Is this familiar?

matrix%282%2C1%2C%0D%0A%0D%0Alim%2C%0D%0A%22x-%3En%22pi%29%28tan%283x%29%2Ftan%28x%29%29

Numerator and denominator both approach 0, so we
can use L'hopital's rule:

matrix%282%2C1%2C%0D%0A%0D%0Alim%2C%0D%0A%22x-%3En%22pi%29%283sec%5E2%283x%29%2F%28sec%5E2%28x%29%29%29

Using reciplocal identity

matrix%282%2C1%2C%0D%0A%0D%0Alim%2C%0D%0A%22x-%3En%22pi%29%283cos%5E2%28x%29%2F%28cos%5E2%283x%29%29%29 = 3

That's the start of the way to do it by calculus.
I'll finish it if you tell me whether you're 
taking calculus or just trig.

Edwin