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

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

Prove that (a sin(B-C))/(b^(2)-c^(2))=(b sin(C-A))/(c^(2)-a^(2))=(c sin(A-B))/(a^(2)-b^(2))

Prove that, |(2a, a-b-c,2a),(2b,2b,b-c-a),(c-a-b,2c,2c)|=(a + b+c)^3

In any triangle ABC, prove that : (a sin(B-C))/(b^2-c^2)= (b sin (C-A))/(c^2-a^2)= (c sin (A-B))/(a^2-b^2) .

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 a Delta ABC, prove that (a sin(B - C))/(b^(2) - c^(2)) = (b sin (C - A))/(c^(2) - a^(2)) = (c sin (A - B))/(a^(2) - b^(2))

Prove that: |{:(-2a, a+b, a+c), (b+a,-2b,b+c),(c+a, c+b,-2c):}|=4(a+b)(b+c)(c+a)

Prove that |a b+c a^2b c+a b^2c a+b c^2|=-(a+b+c)xx(a-b)(b-c)(c-a)dot