" Ho.5."[" Prics affite "],[qquad tan^(-1)a+tan^(-1)b=cos^(-1)(1-ab)/(sqrt([(1+a^(2))(1+b^(2))]))]

Prove that : tan^(-1) a - tan^(-1) b = cos ^(-1) [(1+ab)/(sqrt((1+a^(2))(1+b^(2))))]

Prove that : tan^(-1) a - tan^(-1) b = cos ^(-1) [(1+ab)/(sqrt((1+a^(2))(1+b^(2))))]

Prove that, tan^(-1)a+tan^(-1)b+tan^(-1)((1-a-b-ab)/(1+a+b-ab))=(pi)/(4) .

cos^(-1).(2)/(sqrt(5)) + tan^(-1).(1)/(3) =

Prove that 2tan^(-1)sqrt((b)/(a))=cos^(-1)((a-b)/(a+b))

cos^(-1)""((2)/(sqrt(5))) + tan^(-1)""((1)/(3)) =

tan[tan^(-1)(1/(a+b))+tan^(-1)(b/(a^(2)+ab+1))]=

Prove that tan ^(-1) ""(1)/(4) + tan ^(-1) ""(2)/(9) = cos ^(-1) ((2)/(sqrt5))

The expression (1)/(sqrt(2)){(sin tan^(-1)cos tan^(-1)t)/(cos tan^(-1)sin cot^(-1)sqrt(2)t)}*{sqrt((1+2t^(2))/(2+t^(2)))}