If the two curves y =a^x and y=b^x intersect at angle , then =

Step-by-step solution

Given y=a^x, y=b^x a ^ x = b ^ x x = o curves y = a ^ x and y = b ^ x intersects at x = O , y =1 Let ₁ be the angle made by the tangent of y = a ^ x at x =0 with x axis aligned & slope =m₁= ₁= . d y d x |_ x=0 = .a^x a |_ x=0 & = a aligned Let ₂ be the angle made by the tangent of y=b^x at x=0 with x axis aligned & slope =m₂= ₂= . d y d x |_ x=0 = .b^x b |_ x=0 & = b aligned Given angle between curves 2 aligned & ₁- ₂= & = ₁- ₂ 1+ ₁ ₂ & = m₁-m₂ 1+m₁ m₂ & a= a- b 1+ a b aligned