If `a , b , c >0` and `s=(a+b+c)/2,p rov et h a t` `tan^(-1)sqrt((2a s)/(b c))+tan^(-1)sqrt((2b s)/(c a))+tan^(-1)sqrt((2c s)/(a b))=pi`

If a , b , c >0 and s=(a+b+c)/2 , prove that tan^(-1)sqrt((2a s)/(b c))+tan^(-1)sqrt((2b s)/(c a))+tan^(-1)sqrt((2c s)/(a b))=pi

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'

If a ,\ b ,\ c >0 such that a+b+c=a b c , find the value of tan^(-1)a+tan^(-1)b+tan^(-1)c .

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

Tangents are drawn to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1,(a > b), and the circle x^2+y^2=a^2 at the points where a common ordinate cuts them (on the same side of the x-axis). Then the greatest acute angle between these tangents is given by (A) tan^(-1)((a-b)/(2sqrt(a b))) (B) tan^(-1)((a+b)/(2sqrt(a b))) (C) tan^(-1)((2a b)/(sqrt(a-b))) (D) tan^(-1)((2a b)/(sqrt(a+b)))

In a A B C , , if C is a right angle, then tan^(-1)(a/(b+c))+tan^(-1)(b/(c+a))=

tan^(-1)sqrt(3)-cot^(-1)(-sqrt(3)) is equal to (A) pi (B) -pi/2 (C) 0 (D) 2sqrt(3)

In any Delta ABC,angleB=90^(@) , prove that "tan"(A)/(2)=sqrt((b-c)/(b+c))

In DeltaABC , if /_C = 90^0 , then prove that tan (A/2) = sqrt((c-b)/(c+b)) = a/(b+c)

sum_(r=1)^nsin^(-1)((sqrt(r)-sqrt(r-1))/(sqrt(r(r+1)))) is equal to (a) tan^(-1)(sqrt(n))-pi/4 (b) tan^(-1)(sqrt(n+1))-pi/4 (c) tan^(-1)(sqrt(n)) (d) tan^(-1)(sqrt(n)+1)