Algebra Arithmetic Math Olympiad PRMO

Trigonometry Problem | PRMO 2016 | Question 14

Try this beautiful problem from the Pre-RMO, 2019 based on Trigonometry Problem. You may use sequential hints to solve the problem.

Try this beautiful problem from the PRMO, 2016 based on trigonometry and nearest integer.

Trigonometry and nearest integer – PRMO 2016

If x=cos1cos2cos3…..cos89 and y=cos2cos6cos10….cos86 then find the integer nearest to \(\frac{2}{7}log_{2}(\frac{y}{x})\)

  • is 107
  • is 19
  • is 840
  • cannot be determined from the given information

Key Concepts

Nearest Integer



Check the Answer

Answer: is 19.

PRMO, 2016, Question 14

Plane Trigonometry by Loney

Try with Hints

First hint

\(\frac{y}{x}\)=\(\frac{cos2cos6cos10…..cos86}{cos1cos2cos3…..cos89}\)=\(2^{44}{2}^\frac{1}{2}\frac{cos2cos6cos10……cos86}{sin2sin4…….sin88}\)=\(2^\frac{89}{2}\frac{sin4sin8…….sin88}{sin2sin4……sin88}\)=\(\frac{2^\frac{89}{2}}{cos4cos8cos12…..cos88}\)=\(\frac{(2)^\frac{89}{2}}{(\frac{1}{2})^{22}}\) for given condition by question =\(2^\frac{133}{2}\)

Second Hint


Final Step

=\(\frac{2}{7} \times \frac{133}{2}\)=19.

Subscribe to Cheenta at Youtube

Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.