CBSE BoardEnglish MediumSTD 11 ScienceApplied MathsStraight Lines1 Mark
Question
The angle between the lines whose slopes are $(2-\sqrt{3})$ and $(2+\sqrt{3})$ is ___________ .
✓
Answer
$60^{\circ}$, because Let the slopes of the two lines are $m_1=2-\sqrt{3}$ and $m_2=(2+\sqrt{3})$. Then, acute angle '$\theta$' between the lines is given by $\theta=\tan ^{-1} \frac{m_2-m_1}{1+m_1 m_2}$ $=\tan ^{-1} \frac{(2+\sqrt{3})-(2-\sqrt{3})}{1+(2-\sqrt{3})(2+\sqrt{3})}$ $\begin{array}{l}=\tan ^{-1} \frac{2 \sqrt{3}}{1+4-3} \\ =\tan ^{-1}(\sqrt{3}) \\ =\tan ^{-1}\left(\tan 60^{\circ}\right) \\ =60^{\circ} .\end{array}$
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