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SMO 2011 Open Round 1 Question 5

SMO · SMO 2011 Open Round 1

Question 5

Given $\dfrac{\cos^4\alpha}{\cos^2\beta}+\dfrac{\sin^4\alpha}{\sin^2\beta}=1$, evaluate $\dfrac{\cos^4\beta}{\cos^2\alpha}+\dfrac{\sin^4\beta}{\sin^2\alpha}$.