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

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: tan^(-1) (1/2tan2A) + tan^(-1) (cotA) + tan^(-1) (cot^3A) =0

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

Let a, b and c be positive real numbers. Then prove that tan^(-1) sqrt((a(a + b + c))/(bc)) + tan^(-1) sqrt((b (a + b + c))/(ca)) + tan^(-1) sqrt((c(a + b+ c))/(ab)) =' pi'

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

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

The solution of the differential equation (1+x^2)(dy)/(dx)+1+y^2=0, is a) tan^(-1)x-tan^(-1)y=tan^(-1)C b) tan^(-1)y-tan^(-1)x=tan^(-1)C c) tan^(-1)y+-tan^(-1)x=tan^(\ )C d) tan^(-1)y+tan^(-1)x=tan^(-1)C

Prove that |{:(1,,ab,,(1)/(a)+(1)/(b)),(1 ,,bc,,(1)/(b)+(1)/(c)),( 1,, ca,,(1)/(c)+(1)/(a)):}|=0

1/(bc)+1/(ca)+1/(ab)=

Prove that (1)/(a) + (1)/(b) + (1)/(c ) ge (1)/(sqrt((bc))) + (1)/(sqrt((ca))) + (1)/(sqrt((ab))) , where a,b,c gt 0