If `1/(a+c)+1/(b+c)=3/(a+b+c)`,show that C=`60^@`

If 1/(a+b),1/(b+c),1/(c+a) are in A.P., then c^2,a^2,b^2 are in A.P.

If(a + b + c)(b + c-a) = 3bc in /_\ABC , prove that A = 60^@

If (b-c)^2,(c-a)^2,(a-b)^2 are in A.P. show that 1/(b-c),1/(c-a),1/(a-b) are also in A.P.

If (tan A + sec A) (tan B + sec B) (tan C + sec C) = (tan A -sec A) (tan B -secB) (sec C-tan C),show that each side is equal to +-1

In the formula, a^3+b^3+c^3-3 abc = (a+b+c)(a^2+b^2+c^2-ab-bc-ca) if a + b + c = 0 , then show that a^3 + b^3 + c ^3 = 3 abc

If logp/(b-c)=logq/(c-a)=logr/(a-b) ,then prove that p^a.q^b.r^c=1

If logx/(a+b-2c)=logy/(b+c-2a)=logz/(a+c-2b) , then prove that xyz=1

In the formula, a^3+b^3+c^3-3 abc = 1/2 (a+b+c){(a-b)^2+(b-c)^2+(c-a)^2} , if a + b + c != 0 , Show that if a^3 +b^3+c^3= 3abc impliesa=b=c

If A + B + C= pi and cos A = cos B cos C, show that tan A =tan B + tan C and cot B cot C=1/2.

If a + b + c = 0 , then prove that (a^2+b^2+c^2)/(a^3+b^3+c^3)+2/3(1/a+1/b+1/c)=0