MathDB
2009 Algebra #6 - Sum of Ratios Given Trig Relationships

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January 2, 2012
ratiotrigonometryLaTeX

Problem Statement

Let xx and yy be positive real numbers and θ\theta an angle such that θ≠π2n\theta \neq \frac{\pi}{2}n for any integer nn. Suppose sin⁡θx=cos⁡θy\frac{\sin\theta}{x}=\frac{\cos\theta}{y} and cos⁡4θx4+sin⁡4θy4=97sin⁡2θx3y+y3x. \frac{\cos^4 \theta}{x^4}+\frac{\sin^4\theta}{y^4}=\frac{97\sin2\theta}{x^3y+y^3x}. Compute xy+yx.\frac xy+\frac yx.
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