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

Prove that 2/(b+c)+2/(c+a)+2/(a+b) 0.

In Delta ABC , prove that (a - b)^(2) cos^(2).(C)/(2) + (a + b)^(2) sin^(2).(C)/(2) = c^(2)

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))

If c^(2) = a^(2) + b^(2) , then prove that 4s (s - a) (s - b) (s - c) = a^(2) b^(2)

If a ,b ,a n dc are in H.P., then th value of ((a c+a b-b c)(a b+b c-a c))/((a b c)^2) is ((a+c)(3a-c))/(4a^2c^2) b. 2/(b c)-1/(b^2) c. 2/(b c)-1/(a^2) d. ((a-c)(3a+c))/(4a^2c^2)

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

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

Prove that =|1 1 1 a b c b c+a^2a c+b^2a b+c^2|=2(a-b)(b-c)(c-a)

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

Prove that (b^2+c^2)/(b+c)+(c^2+a^2)/(c+a)+(a^2+b^2)/(a+b)> a+b+c