a line make intercept a and b on the coordinate axes.now axis is rotated by angle x.now that line make equal intercept on the new coordinate axis.what is the value of tanx

Dear Manoj

equation of line in first co ordinate system

x/a  +y/b =i

let new coordinaate system are x' and y'

so x' =xcosΘ +ysinΘ

   y' = ycosΘ -xsinΘ

so equation of line in new co ordinate system

x'/c +y'c =1

now put value of x' and y'

x(cosΘ -sinΘ)/c  + y( sinΘ + cosΘ)/c =1

these two line are same

so  (cosΘ -sinΘ)  =c/a

    ( sinΘ + cosΘ) =c/b

 solve these two

tan Θ =(a-b)/(a+b)

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