If \( \tan \alpha = \frac{1}{\sqrt{3}} \) and tan \(y + \frac{1}{y} = 3\), then what is the value of cos (α + β) ?
If \( a + \frac{1}{a} = 2 \) and\( b+ \frac{1}{b} = -2 \) , then what is the value of \( a^2 + \frac{1}{a^2} + b^2 + \frac{1}{b^2} \) ?