Lu - Uxty虱硐u+ vτα y=1-uv – InterviewSolution

1.	Lu - Uxty虱硐u+ vτα y=1-uv
Answer» taking tan^-1 to both the sides if x = u+v/(1-uv) => tan^-1(x) = tan^(u+v)/(1-uv) = tan^-1(u) + tan^-1(v) similarly tan^-1(y) = tan^-1(u) - tan^-1(v) now adding both tan^-1(x) + tan^-1(y) = tan^-1(x+y)/(1-xy) => tan^-1(u) +tan^-1(v) +tan^-1(u) -tan^-1(v) = tan^-1(x+y)/(1-xy) => 2tan^-1(u) = tan^-1(x+y)/(1-xy)=> tan^-1(2u/1-u²) = tan^-1(x+y)/(1-xy) so, (x+y)/(1-xy) = 2u/(1-u²)

Lu - Uxty虱硐u+ vτα y=1-uv

Answer»

taking tan^-1 to both the sides

if x = u+v/(1-uv)

=> tan^-1(x) = tan^(u+v)/(1-uv) = tan^-1(u) + tan^-1(v) similarly tan^-1(y) = tan^-1(u) - tan^-1(v)

now adding both tan^-1(x) + tan^-1(y) = tan^-1(x+y)/(1-xy) => tan^-1(u) +tan^-1(v) +tan^-1(u) -tan^-1(v) = tan^-1(x+y)/(1-xy)

=> 2tan^-1(u) = tan^-1(x+y)/(1-xy)=> tan^-1(2u/1-u²) = tan^-1(x+y)/(1-xy)

so, (x+y)/(1-xy) = 2u/(1-u²)