In triangle `A B C ,2a csin(1/2(A-B+C))` is equal to `a^2+b^2-c^2` (b) `c^2+a^2-b^2` (c) `b^2-c^2-a^2` (d) `c^2-a^2-b^2`

In any triangle ABC ,c^2 sin 2 B + b^2 sin 2 C is equal to

If D is the mid-point of the side B C of triangle A B C and A D is perpendicular to A C , then (a) 3b^2=a^2-c (b) 3a^2=b^2 3c^2 b^2=a^2-c^2 (d) a^2+b^2=5c^2

With usual notations, in triangle A B C ,acos(B-C)+bcos(C-A)+c"cos"(A-B) is equal to(a) (a b c)/R^2 (b) (a b c)/(4R^2) (c) (4a b c)/(R^2) (d) (a b c)/(2R^2)

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

If Delta represents the area of acute angled triangle ABC, then sqrt(a^2b^2-4Delta^2)+sqrt(b^2c^2-4Delta^2)+sqrt(c^2a^2-4Delta^2)= (a) a^2+b^2+c^2 (b) (a^2+b^2+c^2)/2 (c) a bcosC+b ccosA+c acosB (d) a bsinC+b csinA+c asinB

In triangle ABC , a (b^2 +c^2 ) cos A + b (c^2 +a^2 ) cos B + c(a^2 +b^2 ) cos C is equal to

In any triangle prove that a^2 =(b+c)^2 sin^2 (A/2) +(b-c)^2 cos^2 (A/2)

A plane makes intercepts O A ,O Ba n dO C whose measurements are a,b and c on the O X ,O Ya n dO Z axes. The area of triangle A B C is a. 1/2(a b+b c+c a) b. 1/2a b c(a+b+c) c. 1/2(a^2b^2+b^2c^2+c^2a^2)^(1//2) d. 1/2(a+b+c)^2

Show that: |b^2+c^2a b a c b a c^2+a^2b cc a c b a^2+b^2|=4a^2b^2c^2

Suppose A, B, C are defined as A=a^2b+a b^2-a^2c-a c^2, B=b^2c+b c^2-a^2b-a b^2, and C=a^2c+a c^2-b^2c-b c^2, w h e r ea > b > c >0 and the equation A x^2+B x+C=0 has equal roots, then a ,b ,c are in AdotPdot b. GdotPdot c. HdotPdot d. AdotGdotPdot