ISL 91

Unread post by **Phlembac Adib Hasan** » Sun Jun 03, 2012 5:34 pm

SANZEED wrote:They are odd integers. Sorry for eliminating.

It's ok.Don't do so in the contest.

Unread post by **Phlembac Adib Hasan** » Sun Jun 03, 2012 5:37 pm

sakibtanvir wrote:
Phlembac Adib Hasan wrote:
sakibtanvir wrote:Converting radian into degree,we get,\[cos(540a)+2cos(360a)=0\]
\[Or,cos(180a)+2cos0=0\]
\[Or,cos(180a)=-2\]
Contradiction.....
Who said $a$ is an integer?It's rational only.
\[-1<cos\angle x<1\] for any value of $x$ .
So there is no real value of $a$.

What?Please read the problem carefully:

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 $a$.

Unread post by **SANZEED** » Mon Jun 04, 2012 12:01 am

Clearly I have shown the steps. They imply that $a=\frac{2}{3}$.

Unread post by **Phlembac Adib Hasan** » Mon Jun 04, 2012 7:54 am

SANZEED wrote:Clearly I have shown the steps. They imply that $a=\frac{2}{3}$.

I don't realize why sakibtanvir concluded to that thing where solution was given.

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