4x + 3y - 5 =0 এবং 2y - x + 3 = 0 রেখা দুটির অন্তর্ভুক্ত সূক্ষ্মকোণ θ হলে tanθ এর মান কত ?  

4x + 3y - 5 = 0

2y - x + 3 = 0

3y = -4x + 5

y = -\frac{4}{3}x + \frac{5}{3}

m_1 = -\frac{4}{3}

2y = x - 3

y = \frac{1}{2}x - \frac{3}{2}

m_2 = \frac{1}{2}

\theta

tan \theta

tan \theta = \left| \frac{m_1 - m_2}{1 + m_1 m_2} \right|

tan \theta = \left| \frac{-\frac{4}{3} - \frac{1}{2}}{1 + (-\frac{4}{3})(\frac{1}{2})} \right|

tan \theta = \left| \frac{-\frac{8}{6} - \frac{3}{6}}{1 - \frac{4}{6}} \right|

tan \theta = \left| \frac{-\frac{11}{6}}{\frac{2}{6}} \right|

tan \theta = \left| -\frac{11}{2} \right|

tan \theta = \frac{11}{2}

\frac{11}{2}