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AMO 2021 – Junior College (Grades 11–12) Question 3

AMO · AMO 2021 – Junior College (Grades 11–12)

Question 3

Acute angles $\alpha,\beta$ satisfy $2\tan\alpha+3\sin\beta=7$ and $\tan\alpha-6\sin\beta=1$. Find $\sin\alpha$.

Question illustration
  1. $\frac13$
  2. $\frac{3\sqrt{10}}{10}$
  3. $\frac{3\sqrt7}{7}$
  4. $\frac{5\sqrt5}{5}$
  5. $\frac{10}{9}$