IF` A+B+C=pi`,then prove that `tan (A/2)tan(B/2)+tan(B/2)tan(C/2)+tan(C/2)tan(A/2)=1`

If A+B+C=pi, prove that tan^2(A/2)+tan^2(B/2)+tan^2(C/2)geq1.

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

In any triangle A B C , prove that following : c/(a+b)=(1-tan(A/2)tan(B/2))/(1+tan(A/2)tan(B/2))

Prove that (r+r1)tan((B-C)/2)+(r+r2)tan((C-A)/2)+(r+r3)tan((A-B)/2)=0

If A+B+C=pi, then the value of (tan ""A/2 tan ""B/2+tan ""B/2 tan ""C/2 + tan ""C/2 tan ""A/2) is-

If alpha+beta+gamma=2pi, then (a) tan(alpha/2)+tan(beta/2)+tan(gamma/2)=tan(alpha/2)tan(beta/2)tan(gamma/2) (b) tan(alpha/2)tan(beta/2)+tan(beta/2)tan(gamma/2)+tan(gamma/2)tan(alpha/2)=1 (c) tan(alpha/2)+tan(beta/2)+tan(gamma/2)=-tan(alpha/2)tan(beta/2)tan(gamma/2) (d)none of these

In triangle A B C , if |[1, 1, 1],[cot(A/2),cot(B/2),cot(C/2)],[tan(B/2)+tan(C/2),tan(C/2)+tan(A/2),tan(A/2) +tan(B/2)]| =0 then the triangle must be a. equilateral b. isosceles c. obtuse angled d. none of these

Prove that, tan 1^(@) tan 2^(@) tan 3^(@).....tan 87^(@) tan 88^(@) tan 89^(@) = 1 .

If the angles of a triangle be, A,B,C and cos theta (sin B+ sin C) = sin A , prove that "tan"^(2)( theta)/(2)="tan" (B)/(2) "tan"(C)/(2)

Prove that, tan (B - C) + tan (C -A ) + tan (A -B) = tan (B-C) tan (C-A) tan (A -B)