Question

what is formula for tan inverse x minus tan inverse y = ? , if xy = 1

Answer 1

he answer is............


tan^-1 (x) + tan^-1 (y) = tan^-1 [(x+y) / (1-x*y)]

and ,.

x y = 1


tan^-1 (1/y) + tan^-1 (1/x)


= tan^-1 [(1/y+1/x)/(1-1/y*1/x)]

= tan^-1{[(x+y/(xy)/(1-1/(xy)}

put xy= 1

= tan^-1 {[(x+y/(1))/(1-1/(1)]}

= Tan^-1{[(x+y)/(1-1)]}