(i) tan-1x + tan-1y = tan-1((x+y)/(1-xy)), xy < 1.(ii) tan-1x - tan-1y = tan-1((x-y)/(1+xy)), xy > -1.

(i) tan-1x + tan-1y = tan-1((x+y)/(1-xy)), xy < 1.Let tan-1x = A and tan-1y = BÞ tan A = x and tan B = yNow, tan(A+B) = (tanA + tanB)/(1-tanAtanB)? tan(A+B) = (x+y)/(1-xy)?tan-1[(x+y)/(1-xy)] = A + B?tan-1[(x+y)/(1-xy)] = tan-1x + tan-1y(ii) tan-1x - tan-1y = tan-1((x-y)/(1+xy)), xy > -1.Proof:Let tan-1x = a ? x = tan a tan-1y = ß ? y = tan ßNow, tan(a - ß) = (tan a - tan ß)/(1+ tanatanß) = (x-y)/(1+xy)2:43 AM 5/5/2016676563:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:25 AM 5/5/20163:26 AM 5/5/20163:26 AM 5/5/20163:26 AM 5/5/20163:26 AM 5/5/20163:26 AM 5/5/20163:26 AM 5/5/20163:26 AM 5/5/20163:26 AM 5/5/20163:26 AM 5/5/20163:26 AM 5/5/20163:26 AM 5/5/20163:26 AM 5/5/20163:26 AM 5/5/20163:26 AM 5/5/20163:26 AM 5/5/20163:26 AM 5/5/20163:26 AM 5/5/20163:26 AM 5/5/20163:26 AM 5/5/20163:26 AM 5/5/2016a - ß = tan-1 [(x-y)/(1+xy)]tan-1x - tan-1y = tan-1 [(x-y)/(1+xy)]Hence, tan-1x - tan-1y = tan-1 [(x-y)/(1+xy)], xy > -1