A Trig Elimination

★ 7/10trigonometry Substitution algebra Trigonometric Identities

Problem

Let $x, y \in \mathbb{R}$ and $\theta \in \left(\dfrac{\pi}{4}, \dfrac{\pi}{2}\right)$ satisfy

\frac{\sin\theta}{x} = \frac{\cos\theta}{y}, \qquad \frac{\cos^2\theta}{x^2} + \frac{\sin^2\theta}{y^2} = \frac{10}{3\left(x^2 + y^2\right)}.

Find $\dfrac{x}{y}$ .

Answer

Solution

Difficulty	7/10
Topics	trigonometry, Substitution, algebra, Trigonometric Identities

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