Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation

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Problem B. 4008. (May 2007)

B. 4008. Prove that

${\rm cot}\, 70^{\circ} + 4 \cos 70^{\circ} = \sqrt{3}.$

(3 pont)

Deadline expired on June 15, 2007.

Sorry, the solution is available only in Hungarian. Google translation

Megoldás: Az egyenlőség ekvivalens a $4\cos 70^\circ \sin70^\circ=\sqrt{3}\sin70^\circ-\cos 70^\circ$ egyenlőséggel. Mivel 2sin 70^ocos 70^o=sin 140^o=sin 40^o, a bizonyítandó állítást

$\sin40^\circ=\frac{\sqrt{3}}{2}\sin70^\circ-\frac{1}{2}\cos 70^\circ$

alakban is felírhatjuk. Lévén $\cos30^\circ=\sqrt{3}/2$ és sin 30^o=1/2, a jobboldalon éppen sin (70^o-30^o) áll.

Statistics:

107 students sent a solution.

3 points: 101 students.

0 point: 1 student.

Unfair, not evaluated: 5 solutionss.

Problems in Mathematics of KöMaL, May 2007

107 students sent a solution.
3 points:	101 students.
0 point:	1 student.
Unfair, not evaluated:	5 solutionss.