If ``cos, (A)/2 cos, (B-C)/2 + cos, B/2 cos, (C-A)/2 + cos, C/2 cos, (A-B)/2 = sinA +sinB+sinC`

If A+B+C= pi/2 , show that : cos^2 A + cos^2 B + cos^2 C = 2 + 2 sinA sinB sinC .

If A+B+C=180^0 , prove that : cos^2 (A/2) + cos^2 (B/2) - cos^2 (C/2) = 2cos (A/2) cos (B/2) sin (C/2)

In any DeltaABC , prove that : (cos A)/(b cos C + c cos B) + (cos B)/(c cos A + a cos C) + (cos C)/(a cos B + b cos A) = (a^2 + b^2 + c^2)/(2abc)

Prove that : (sin 2A+sin 2B + sin 2C)/(cos A + cos B + cos C-1) = 8 cos(A/2) cos( B/2) cos( C/2)

Prove that: cos^2A+cos^2B-2cosA\ cos B cos\ (A+B)=sin^2(A+B)

Prove that: cos^2A+cos^2B-2cosA\ cos B cos\ (A+B)=sin^2(A+B)

In any DeltaABC , prove that : a cos A + b cos B + c cos C = 2a sin B sin C

If A+B+C=2S , prove that : cos^2 S + cos^2 (S-A) + cos^2 (S-B) + cos^2 (S-C) = 2+2cosA cosB cosC .

If in a triangle ABC, (1 + cos A)/(a) + (1 + cos B)/(b) + (1+ cos C)/(c) = (k^(2) (1 + cos A) (1 + cos B) (1 + cos C))/(abc) , then k is equal to

If I is the incenter of a triangle ABC, then the ratio I A : I B : I C is equal to (a) cos e c A/2: cos e c B/2: cos e c C/2 (b) sinA/2:sinB/2:sinC/2 (c) secA/2:secB/2:secC/2 (d) none of these