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a line has intercepts a and b on the coordinate axis when the axes are rotated through an angle θ,keeping the origin fixed the line makes equal intercepts on the coordinate axes then tanθ=?
When the axes are rotated through an angle θ,keeping the origin fixed then the graph looks like this:
Solving the eqns. x/a + y/b =1 with
we will get,
x = ab/(b + atanθ), y = abtanθ/(atanθ + b)
AND
x = ab/(b - acotθ), y = abcotθ/(acotθ - b) as therir points. of intersections.
Now, it is said that the intercepts made by the line are equal.
Thus, ab/(b + atanθ) = abcotθ/(acotθ - b)
solving this , it will reduce to
tanθ = (a-b)/(a+b)
is the answer.
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