Unit-I: Sets and Functions
Unit-II: Algebra
Unit-III: Coordinate Geometry
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability

Angle between a pair of intersecting lines

If  \phi measures an angle between the intersecting lines  L_1 and  L_2 , with slopes respectively m_1 and  m_2 , then

\tan\phi= \pm \dfrac{m_1- m_2}{1+m_1m_2}

Example:

Let m_1=\dfrac{1}{\sqrt{3}}   and  m_2 =1   are slopes of  L_1   and  L_2 then,

\begin{aligned} \tan \phi&= \pm \dfrac{\dfrac{1}{\sqrt{3}}-1}{1+\dfrac{1}{\sqrt{3}}\cdot1}=\pm\dfrac{\tan \dfrac{\pi}{6}- \tan \dfrac{\pi}{4}}{1+ \tan \dfrac{\pi}{6}\cdot \tan\dfrac{\pi}{4}}\\&=-\tan \left( \dfrac{\pi}{6}-\dfrac{\pi}{4} \right)\\&=-\tan\left( \dfrac{2\pi-3\pi}{12} \right)\\&=\tan \dfrac{\pi}{12}\end{aligned}

 \therefore \phi = \dfrac{\pi}{12}

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