MathDB

27

Part of 2008 National Olympiad First Round

Problems(1)

Turkey NMO 2008 1st Round - P27 (Algebra)

Source:

8/26/2012
The angles α,β,γ\alpha, \beta, \gamma of a triangle are in arithmetic progression. If sin⁡20α\sin 20\alpha, sin⁡20β\sin 20\beta, and sin⁡20γ\sin 20\gamma are in arithmetic progression, how many different values can α\alpha take?
<spanclass=′latex−bold′>(A)</span> 1<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 3<spanclass=′latex−bold′>(D)</span> 4<spanclass=′latex−bold′>(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}
trigonometryarithmetic sequence