Question : If $\tan \alpha=\frac{1}{\sqrt{3}}$ and $\tan \beta=\sqrt{3}$ then what is the value of $\cos (\alpha+\beta)$?
Option 1: 0.2
Option 2: 0
Option 3: 0.5
Option 4: 1
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Correct Answer: 0
Solution :
$\tan \alpha=\frac{1}{\sqrt{3}}$
⇒ $\alpha = 30^{\circ}$
$\tan \beta=\sqrt{3}$
⇒ $ \beta = 60^{\circ}$
So, $\cos (\alpha+\beta)$
= $\cos (30^{\circ}+60^{\circ})$
= $\cos (90^{\circ}) = 0$
Hence, the correct answer is 0.
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