Find the angle between the lines whose slopes are \(\sqrt 3 \ and \frac{1}{\sqrt 3}\)

CONCEPT:

If α is the acute angle between two non-vertical and non-perpendicular lines L₁ and L₂ with slopes m₁ and m₂ respectively then \(\tan α = \left| {\frac{{{m_2} - {m_1}}}{{1 + {m_1} \cdot {m_2}}}} \right|\)

CALCULATION:

Here, we have to find the angle between the lines whose slopes are \(\sqrt 3 \ and \frac{1}{\sqrt 3}\)

Let \(m_1 = \sqrt 3 \ and \ m_2 = \frac{1}{\sqrt 3}\)

As we know that, \(\tan α = \left| {\frac{{{m_2} - {m_1}}}{{1 + {m_1} \cdot {m_2}}}} \right|\)

⇒ \(\tan α = \left| {\frac{{{\frac{1}{\sqrt 3}} - {\sqrt 3}}}{{1 + {\sqrt 3} \cdot {\frac{1}{\sqrt 3}}}}} \right| \)

⇒ \(tan \ α = \frac{1}{\sqrt3}\)

⇒ α = 30°

So, the angle between the lines whose slopes are \(\sqrt 3 \ and \frac{1}{\sqrt 3}\) is 45° 

Hence, option C is the correct answer.