TrigIdentity AM/GM Intermediate

Problem - 2295

Let $\alpha, \beta \in (0, \frac{\pi}{2})$. Show that $\alpha + \beta = \frac{\pi}{2}$ if and only if $$\frac{\sin^4 \alpha}{\cos^2 \beta} + \frac{\cos^4\alpha}{\sin^2\beta} = 1$$

The solution for this problem is available for $0.99.
You can also purchase a pass for all available solutions for $99.