((50))/(4b^(2)c^(2))

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

The expression : ((a+b+c)(b+c-a)(c+a-b)(a+b-c))/(4b^(2)c^(2)) is :

Factorise : a^(4)(b^(2)-c^(2))+b^(4)(c^(2)-a^(2))+c^(4)(a^(2)-b^(2))

|(1,a^(2),a^(4)),(1,b^(2),b^(4)),(1,c^(2),c^(4))|=(a+b)(b+c)(c+a)|(1,1,1),(a,b,c),(a^(2),b^(2),c^(2))|

If b is the mean proportion between a and c, show that : (a^(4)+a^(2)b^(2)+b^(4))/(b^(4)+b^(2)c^(2)+c^(4))=a^(2)/c^(2)

In any Delta ABC,((a+b+c)(b+c-a)(c+a-b)(a+b-c))/(4b^2c^2) =

If a + b + c = 0 , prove that a^(4) + b^(4) + c^(4) = 2(b^(2)c^(2)+c^(2)a^(2)+a^(2)b^(2)) = 1//2 (a^(2) + b^(2) + c^(2))^(2)