" (c) Prove: "tan^(-1)a+cot^(-1)b=cot^(-1)(b-a)/(1+ab)

Prove that tan(cot^(-1)x)=cot(tan^(-1)x)

Prove that tan(cot^(-1)x)=cot(tan^(-1)x)

Prove that tan(cot^(-1)x)=cot(tan^(-1)x)

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

Prove that: cot^(-1)((ab+1)/(a-b))+cot^(-1)((bc+1)/(b-c))+cot^(-1)((ca+1)/(c-a))=0 .

Prove that: cot^(-1)((ab+1)/(a-b))+cot^(-1)((bc+1)/(b-c))+cot^(-1)((ca+1)/(c-a))=0

Prove that : cot^(-1)((1+ab)/(a-b))+cot^(-1)((1+bc)/(b-c))+cot^(-1)((1+ca)/(c-a))=pi,(a>b>c>0)

Prove that : cot^(-1)((1+ab)/(a-b))+cot^(-1)((1+bc)/(b-c))+cot^(-1)((1+ca)/(c-a))=pi,(a>b>c>0)

Id a,b,c are distinct non-zero real numbers having the same sign. Prove that Cot^(-1)((ab+1)/(a-b)) +cot^(-1)((bc+1)/(b-c))+ Cot^(-1)((ca+1)/(c-a)) = pi (or) 2 pi .

If cot^(-1)(1/a) + cot^(-1)(1/b) + cot^(-1)(1/c) = 0 .