(c) If `(a)/(b)=(b)/(c)` ,prove that `(a+b+c)(a-b+c)=a^(2)+b^(2)+c^(2)`

Prove that a(b cos C- os B)=b^(2)-c^(2)

If (a)/(b+c)+(b)/(c+a)+(c)/(a+b)=0 then prove that (a^(2))/(b+c)+(b^(2))/(c+a)+(c^(2))/(a+b)=0

prove that b^(2)c^(2)+c^(2)a^(2)+a^(2)b^(2)>=abc(a+b+c)

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)

If f(a,b) =(f(b)-f(a))/(b-a) and f(a,b,c)=(f(b,c)-f(a,b))/(c-a) prove that f(a,b,c)=|{:(f(a),f(b),f(c)),(1,1,1),(a,b,c):}|-:|{:(1,1,1),(a,b,c),(a^(2),b^(2),c^(2)):}| .

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

In Delta ABC, prove that ((a+b+c)(b+c-a)(c+a-b)(a+b-c))/(Ab^(2)c^(2))=sin^(2)A

If a,b,c are in GP, prove that (a^2-b^2)(b^2+c^2)=(b^2-c^2)(a^2+b^2) .

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

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