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Let

$$\frac{\sin x}{\cos y} + \frac{\sin y}{\cos x} = 1 \quad \text{and} \quad \frac{\cos x}{\sin y} + \frac{\cos y}{\sin x} = 6.$$

Find

$$\frac{\tan x}{\tan y} + \frac{\tan y}{\tan x}$$

I have put around 5 hours of my own time into this porblem and I really need help. (Seriously I have the scratch paper to prove it).

Jul 22, 2020