help in proving

[orir]

i need to proof that:
if
|arctanx|<=pi/4
so
|sinx|<2cosx


how do i solve this?
thanks!

 

[pka]

i need to proof that:
if
|arctanx|<=pi/4
so
|sinx|<2cosx

Can you show that \(\displaystyle |\arctan(x)|\le\frac{\pi}{4}\) implies \(\displaystyle |x|\le 1~?\)

Is so, then on that domain you have \(\displaystyle \dfrac{|\sin(x)|}{\cos(x)}=|\tan(x)|<2\)

 

[orir]

thank you! another question if i may..

i need to find a- m (m>0)
so
for every x>m we get that

(x²-2x)/(x+2cosx) > 1000

 

[lookagain]

i need to find a- m (m>0)
so
for every x>m we get that

(x²-2x)/(x+2cosx) > 1000

orir,

please start a new thread for this question and show some work and/or
some ideas of yours about the question.


And please adhere to these rules before posting:

http://www.freemathhelp.com/forum/threads/41538-Read-Before-Posting!!