1. The slopes of two lines are 1/√3 and √3. What is the angle between these two lines?
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By: anil on 05 May 2019 02.14 am
Slope of the two lines, $$m_1=frac{1}{sqrt{3}}$$ and $$m_2=sqrt{3}$$ Let angle between them = $$ heta$$ Then, $$tan( heta)=|frac{m_2-m_1}{1+m_1m_2}|$$ => $$tan( heta) = frac{sqrt{3}-frac{1}{sqrt{3}}}{1+sqrt{3}frac{1}{sqrt{3}}}$$ => $$tan( heta)=frac{tan(60)-tan(30)}{1+tan(60)tan(30)}$$ => $$tan( heta)=tan(60-30)$$ $$ecause [tan(A-B)=frac{tanA-tanB}{1+tanAtanB}]$$ => $$ heta = 30$$° => Ans - (D)
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