Prove that `tan^(-1)((a-b)/(1+ab))+tan^(-1)((b-c)/(1+bc))+tan^(-1)c=tan^(-1)a`

Prove that tan^(-1)((ab)/(1+ab))+tan^(-1)((bc)/(1+bc))+tan^(-1)((ca)/( 1+ca))=0,ab>(-1),bc>(-1),ca>(-1)

Prove that tan^(-1)((ab)/(1+ab))+tan^(-1)((bc)/(1+bc))+tan^(-1)((ca)/( 1+ca))=0,ab>(-1),bc>(-1),ca>(-1)

Prove that tan^(-1)((ab)/(1+ab))+tan^(-1)((bc)/(1+bc))+tan^(-1)((ca)/( 1+ca))=0,ab>(-1),bc>(-1),ca>(-1)

Prove that tan^(-1)((ab)/(1+ab))+tan^(-1)((bc)/(1+bc))+tan^(-1)((ca)/( 1+ca))=0,ab>(-1),bc>(-1),ca>(-1)

If a,b,c>0 and s=(a+b+c)/(2), prove thattan^(-1)sqrt((2as)/(bc))+tan^(-1)sqrt((2bs)/(ca))+tan^(-1)sqrt((2cs)/(ab))=pi

Prove that : tan^(-1)( (a^3 -b^3)/(1+a^3 b^3)) + tan^(-1)( (b^3 - c^3)/(1+b^3 c^3)) + tan^(-1)( (c^3 - a^3)/(1+c^3 a^3)) = 0

Prove that: tan[(pi)/(4)+(1)/(2) tan^(-1)((a)/(b))]+tan[(pi)/(4)-(1)/(2)tan^(-1)((a)/(b))]=(2sqrt(a^(2)+b^(2)))/(b)

If a,b,c are real positive numbers and theta =tan^(-1)[(a(a+b+c))/(bc)]^(1/2)+tan^(-1)[(b(a+b+c))/(ca)]^(1/2)+tan^(-1)[(c(a+b+c))/(ab)]^(1/2) , then tantheta equals

If a,b,c be positive real numbers and the value of theta=tan^(-1)sqrt((a(a+b+c))/(bc))+tan^(-1)sqrt((b(a+b+c))/(ca))+tan^(-1)sqrt((c(a+b+a))/((ab))) then tan theta is equal to