Prove that,
`(asin(B-C))/(b^(2)-c^(2)) = (bsin(C-A))/(c^(2)-a^(2)) = (csin(A-B))/(a^(2)-b^(2))`

In a DeltaABC (bsin(C-A))/(c^(2)-a^(2))+(csin(A-B))/(a^(2)-b^(2))=

If any triangle A B C , that: (asin(B-C))/(b^2-c^2)=(bsin(C-A))/(c^2-a^2)=(csin(A-B))/(a^2-b^2)

In triangleABC , the expression (b^(2)-c^(2))/(asin(B-C)) + (c^(2)-a^2)/(bsin(C-A)) +(a^(2)-b^(2))/(csin(A-B)) is equal to

Prove that : |{:(a^(2),b^(2)+c^(2),bc),(b^(2),c^(2)+a^(2),ca),(c^(2),a^(2)+b^(2),ab):}|=-(a-b)(b-c)(c-a)(a+b+c)(a^(2)+b^(2)+c^(2))

Prove that a(b^(2) + c^(2)) cos A + b(c^(2) + a^(2)) cos B + c(a^(2) + b^(2)) cos C = 3abc

In any triangle A B C , prove that following: \ \ asin(A/2)sin((B-C)/2)+bsin(B/2)sin((C-A)/2)+c sin(C/2)sin((A-B)/2)=0.

In a Delta A B C , prove that: ((b^2-c^2)/(a^2))sin2A+((c^2-a^2)/(b^2))sin2B+((a^2-b^2)/(c^2))sin2C=0

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

Prove that ((a+b+c)(b+c-a)(c+a-b)(a+b-c))/(4b^2c^2)=sin^2A

Prove that : (i) |{:(a,c,a+c),(a+b,b,a),(b,b+c,c):}|=2 abc (ii) Prove that : |{:(a^(2),bc,ac+c^(2)),(a^(2)+ab,b^(2),ac),(ab,b^(2)+bc,c^(2)):}|=4a^(2)b^(2)c^(2)