MathDB
Turkey NMO 2008 1st Round - P27 (Algebra)

Source:

August 26, 2012
trigonometryarithmetic sequence

Problem Statement

The angles α,β,γ\alpha, \beta, \gamma of a triangle are in arithmetic progression. If sin20α\sin 20\alpha, sin20β\sin 20\beta, and sin20γ\sin 20\gamma are in arithmetic progression, how many different values can α\alpha take?
<spanclass=latexbold>(A)</span> 1<spanclass=latexbold>(B)</span> 2<spanclass=latexbold>(C)</span> 3<spanclass=latexbold>(D)</span> 4<spanclass=latexbold>(E)</span> None of the above <span class='latex-bold'>(A)</span>\ 1 \qquad<span class='latex-bold'>(B)</span>\ 2 \qquad<span class='latex-bold'>(C)</span>\ 3 \qquad<span class='latex-bold'>(D)</span>\ 4 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the above}