Trigonometry Problem | PRMO 2016 | Question 14

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

\(\frac{2}{7}log_{2}(\frac{y}{x})\)=\(\frac{2}{7}log_{2}{2}^\frac{133}{2}\)

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