If a `sectheta+bt a ntheta+c=0` and `psectheta+qtantheta+r=0,` prove that `(b r-q c)^2-(p c-a r)^2=(a q-b p)^2`

If a , b and c b respectively the pth , qth and rth terms of an A.P. prove that a(q-r) +b(r-p) +c (p-q) =0

If pth, qth and rth term of an A.P. be a,b,c then prove that. a(q-r)+b(r-p)+c(p-q)=0

If the p^(th), q^(th) and r^(th) terms of a H.P. are a,b,c respectively, then prove that (q - r)/(a) + (r - p)/(b) + (p - q)/(c) = 0

If a,b,c are respectively the sums of p,q,r terms of an A.P., prove that a/p(q-r)+b/q(r-p)+c/r(p-q)=0

Ifa,b,c,p,q,r be six complex numbers such that a/p+b/q+c/r=0 and p/a+q/b+r/c=1-i then prove that (p^2/a^2)+(q^2/b^2)+(r^2/c^2)=-2i

If a,b,c denote the sides of triangleABC , show that the value of the expression, a^3 (p-q)(p-r)+b^2(q-r)+b^2(q-r)(q-p)+c^2(r-p)(r-q) cannot be negative where p,q,r in R .

If a,b,c are respectively the p^(th),q^(th),r^(th) terms of an A.P.,then prove that a(q-r)+b(r-p)+c(p-q)=0

If agt0,bgt0,cgt0 be respectively the pth, qth and rth terms of a G.P. are a, b ,c , prove that : (q-r) log a+ (r -p) log b + (p -q) log c = 0 .

If pnea,qneb,rnec and |{:(p,b,c),(a,q,c),(a,b,r):}|=0 then prove that p/(p-a)+q/(q-b)+r/(r-c)=2

Sum of the first p,q and r terms of an A.P. are a, b and c, respectively. Prove that, (a)/(p) (q-r) + (b)/(q) (r-p) + (c )/(r ) (p-q) = 0