If `pa n dq` are perpendicular from the angular points A and B of ` A B C` drawn to any line through the vertex `C ,` then prove that `a^2b^2sin^2C=a^2p^2+b^2q^2-2a b p qcosCdot`

If the angles A,B,C of a triangle are in A.P. and sides a,b,c, are in G.P., then prove that a^2, b^2,c^2 are in A.P.

If p is the length of perpendicular from the origin onto the plane whose intercepts on the axes area a,b,c then (A) a+b+c=p (B) a^-2+b^-2+c^-2=p^(-2) (C) a^(-1)+b^(-1)+c^(-1)=p^(-1) (D) a^(-1)+b^(-1)+c^(-1)=1

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

For any triangle ABC, prove that (sin(B-C))/(sin(B+C))=(b^(2)-c^(2))/(a^(2))

If a,b,c are in G.P., then show that : (a^2-b^2)(b^2+c^2)=(b^2-c^2)(a^2+b^2)

In any triangle ABC, prove that: (sin(B-C))/(sin(B+C))=(b^(2)-c^(2))/(a^(2))

If a, b, c, d are in G.P., then prove that: (b-c)^(2)+(c-a)^(2)+(d-b)^(2)=(a-d)^(2)

In any Delta ABC, prove that :(b^(2)-c^(2))sin^(2)A+(c^(2)-a^(2))sin^(2)B+(a^(2)-b^(2))sin^(2)C=0

If a,b,c are in G.P., prove that a^(2)+b^(2),ab+bc,b^(2)+c^(2) are also in G.P

In any DeltaABC , prove that (a-b)^(2)cos^(2)""C/2+(a+b)^(2)sin^(2)""C/2=c^(2).