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

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

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

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

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

Prove that tan^-1 (1/4) + tan^-1 (2/9) = 1/2 cos^-1 (3/5) = sin^-1(1/sqrt5)

Prove that tan(pi/4 +1/2 cos^(-1) (a/b)) + tan^(-1) (pi/4 -1/2 cos^(-1) (a/b)) =2b/a

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

Prove that : 2tan^(-1)(sqrt((a-b)/(a+b))tan""x/2)=cos^(-1)((acosx+b)/(a+bcosx)) .

Prove that tan(pi/4+1/2cos^(-1)(a/b))+tan(pi/4-1/2cos^(-1)(a/b))=(2b)/a .

Prove that : "tan"(pi/4 +1/2 "cos"^(-1) a/b) +"tan"(pi/4 -1/2 "cos"^(-1) a/b) =(2b)/a