Show that the tangent of an angle between the lines `(x)/(a)+(y)/(b)=1` and `(x)/(a)-(y)/(b)=1` and `(2ab)/(a^(2)-b^(2))`.
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Given equation of lines are `(x)/(a)+(y)/(b)=1` `therefore` Slope, `m_1=-(b)/(a)` and `(x)/(a)-(y)/(b)=1` `therefore` Slope, `m_2=(b)/(a)` Let `theta` be the angle between the given lines , than `tan theta =|((m_1-m_2))/((1+m_1m_2))|rArr tan theta=|(-b/(a)-b/a)/(1+((-b)/(a))(-(b)/(a)))|` `rArr tantheta=|((-2b)/(a))/((a^2-b^2)/(a^2))|rArrtan theta=(2ab)/(a^2-b^2)`
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