If b is the harmonic mean between a and c, then prove that `(1)/(b - a) + (1)/(b - c) = (1)/(a) + (1)/(c)`

Prove that (cos C + cos A)/(c + a) + (cos B)/(b) = (1)/(b)

Prove that : (r_1)/(b c)+(r_2)/(c a)+(r_3)/(a b)=1/r-1/(2R)

If a is the A.M. between b and c, b the G.M. between a and c, then show that 1/a,1/c,1/b are in A.P.

A+ B = C and tan A = k tan B , then prove that sin (A-B) = (k-1)/(k+1) sin C

If in a triangle A B C ,/_C=60^0, then prove that 1/(a+c)+1/(b+c)=3/(a+b+c) .

If in a triangle A B C ,/_C=60^0, then prove that 1/(a+c)+1/(b+c)=3/(a+b+c) .

In a triangle A B C ,/_C=60^0, then prove that: 1/(a+c)+1/(b+c)=3/(a+b+c)dot

If a (b +c), b (c+a) , c (a +b) are in A.P. , prove that (1)/(a), (a)/(b), (1)/(c ) are also ln A.P.

If a ,b , a n dc are distinct positive real numbers such that a+b+c=1, then prove that ((1+a)(1+b)(1+c))/((1-a)(1-b)(1-c))> 8.

Without expanding at any state, prove that |((1)/(a),a,bc),((1)/(b),b,ca),((1)/(c ),c,ab)|=0