The slopes of two lines are 1 and $$\frac{1}{\sqrt{3}}$$. What is the angle between these two lines?
Slope of the two lines, $$m_1=1$$ and $$m_2=\frac{1}{\sqrt{3}}$$
Let angle between them = $$\theta$$
Then, $$tan(\theta)=|\frac{m_1-m_2}{1+m_1m_2}|$$
=> $$tan(\theta) = \frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}$$
=> $$tan(\theta)=\frac{tan(45)-tan(30)}{1+tan(45)tan(30)}$$
=> $$tan(\theta)=tan(45-30)$$ $$\because [tan(A-B)=\frac{tanA-tanB}{1+tanAtanB}]$$
=> $$\theta = 15$$°
=> Ans - (A)
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