Re: ISL 91
Posted: Sun Jun 03, 2012 5:34 pm
It's ok.Don't do so in the contest.SANZEED wrote:They are odd integers. Sorry for eliminating.
It's ok.Don't do so in the contest.SANZEED wrote:They are odd integers. Sorry for eliminating.
What?Please read the problem carefully:sakibtanvir wrote:\[-1<cos\angle x<1\] for any value of $x$ .Phlembac Adib Hasan wrote:Who said $a$ is an integer?It's rational only.sakibtanvir wrote:Converting radian into degree,we get,\[cos(540a)+2cos(360a)=0\]
\[Or,cos(180a)+2cos0=0\]
\[Or,cos(180a)=-2\]
Contradiction.....
So there is no real value of $a$.
SANZEED wrote:Let $a$ be a rational number with $0\leq a\leq 1$. Suppose that \[cos 3\pi a+2 cos 2\pi a=0\].
(angles are in radians)Determine,with proof,the value of $a$.
I don't realize why sakibtanvir concluded to that thing where solution was given.SANZEED wrote:Clearly I have shown the steps. They imply that $a=\frac{2}{3}$.
