Prove that `(r+r_1)tan((B-C)/2)+(r+r_2)tan((C-A)/2)+(r+r_3)tan((A-B)/2)=0`

Prove that, tan((A)/(2)+B)=(c+b)/(c-b)tan((A)/(2))

In triangle ABC, prove that, tan((B-C)/(2))=(b-c)/(b+c)cot((A)/(2)) tan((C-A)/(2))=(c-a)/(c+a)cot((B)/(2)) tan((A-B)/(2))=(a-b)/(a+b)cot((C)/(2))

Show that (b-c)/(r _(1))+ (c-a)/(r _(2))+(a-b)/(r _(3)) =0.

Prove that ((n),(r))+2((n),(r-1))+((n),(r-2))=((n+2),(r))

Prove the followings : If tan^(-1)((yz)/(xr))+tan^(-1)((zx)/(yr))+tan^(-1)((xy)/(zr))=pi/2 then x^(2)+y^(2)+z^(2)=r^(2) .

Sum of the first p,q and r terms of an A.P. are a, b and c, respectively. Prove that, (a)/(p) (q-r) + (b)/(q) (r-p) + (c )/(r ) (p-q) = 0

If x^2+y^2+z^2=r^2,t h e ntan^(-1)((z y)/(x r))+tan^(-1)((x z)/(y r))+tan^(-1)((x y)/(z r)) is equal to pi (b) pi/2 (c) 0 (d) none of these

Prove that if two bubbles of radii r_(1) and r_(2)(r_(1)ltr_(2)) come in contact with each other then the radius of curvature of the common surface r=(r_(1)r_(2))/(r_(2)-r_(1))

Statement I In a Delta ABC, if a lt b lt c and ri si inradius and r_(1), r_(2) ,r_(3) are the exradii opposite to angle A,B,C respectively, then r lt r_(1) lt r_(2) lt r_(3). Statement II For, DeltaABC r_(1)r_(2)+r_(2)r_(3)+r_(3)r_(1)=(r_(1)r_(2)r_(3))/(r)

Differentiate tan^(-1) ((sqrt(1+x^(2))-1)/(x)) w.r.t tan^(-1)x , where x ne 0