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(a,b,c gt 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)/(b)-"tan"^(-1)((a-b)/(a+b))=(pi)/(4) .

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

Prove that "tan"^(-1)(ap-q)/(aq+p)+"tan"^(-1)(b-a)/(ab+1)+"tan"^(-1)(c-b)/(bc+1)="tan"^(-1)(p)/(q)-"tan"^(-1)(1)/(c )

Prove that 1-tan(A/2)tan(B/2)=(2c)/(a+b+c) .

prove that , tan ^(-1)""(b-c)/(1+bc)+tan^(-1)""(c-a)/(1+ca)+tan ^(-1 )""(a-b )/(1+ab)=0 .

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

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)))

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)

A particle just clears a wall of height b at distance a and strikes the ground at a distance c from the point of projection. The angle of projection is (1) tan^(-1)(b/(a c)) (2) "45"^o (3) tan^(-1)((b c)/(a(c-a))) (4) tan^(-1)((b c)/a)