2021 GCIME Problems/Problem 5
Revision as of 14:45, 6 March 2021 by Sugar rush (talk | contribs) (Created page with "==Problem== Let <math>x</math> be a real number such that<cmath>\frac{\sin^{4}x}{20}+\frac{\cos^{4}x}{21}=\frac{1}{41}</cmath>If the value of<cmath>\frac{\sin^{6}x}{20^{3}}+\f...")
Problem
Let be a real number such thatIf the value ofcan be expressed as where and are relatively prime positive integers, then what is the remainder when is divided by ?
Solution
Let . Then . It is given that By the quadratic formula, and this is the value of . We would like to find . The answer is