The slopes of two lines are 1/√3 and √3. What is the angle between these two lines?

Slope of the two lines, $$m_1=\frac{1}{\sqrt{3}}$$ and $$m_2=\sqrt{3}$$

Let angle between them = $$\theta$$

Then, $$tan(\theta)=|\frac{m_2-m_1}{1+m_1m_2}|$$

=> $$tan(\theta) = \frac{\sqrt{3}-\frac{1}{\sqrt{3}}}{1+\sqrt{3}\frac{1}{\sqrt{3}}}$$

=> $$tan(\theta)=\frac{tan(60)-tan(30)}{1+tan(60)tan(30)}$$

=> $$tan(\theta)=tan(60-30)$$      $$\because [tan(A-B)=\frac{tanA-tanB}{1+tanAtanB}]$$

=> $$\theta = 30$$°

=> Ans - (D)