If `a : b = c : d ` , then prove that `(a + c) : (b + d) = sqrt(a^(2) - c^(2)) : sqrt(b^(2) - d^(2))`

If (a)/(b) = (c)/(d) , show that : (a + b) : (c + d) = sqrt(a^(2) + b^(2)) : sqrt(c^(2) + d^(2))

If a : b = c : d, then show that sqrt(a^(2) + c^(2)) : sqrt(b^(2) + d^(2)) = (pa + qc) : (pb+qd)

If a+c = 2b and 2/c= 1/b+1/d then prove that a:b = c:d.

If : a * cos A-b * sin A=c, "then" : a * sin A +b* cos A= A) sqrt(a^(2)+b^(2)-c^(2)) B) sqrt(a^(2)-b^(2)+c^(2)) C) sqrt(b^(2)+c^(2)-a^(2)) D) sqrt(b^(2)+c^(2)+a^(2))

If x + iy = sqrt((a + ib)/(c + id)) Prove that x^(2) + y^(2) = sqrt(( a^(2) + b^(2))/(c^(2) + d^(2)))

If a, b, c, d are in GP, then prove that 1/((a^(2)+b^(2))), 1/((b^(2)+c^(2))), 1/((c^(2)+d^(2))) are in GP.

If the line segment joining the points P (a,b) and Q(c,d) subtends an angle theta at the origin , then the value of costheta is a) (ab+cd)/(sqrt(a^(2)+b^(2))sqrt(c^(2)+d^(2))) b) (ab)/(sqrt(a^(2)+b^(2)))+(bd)/(sqrt(c^(2)+d^(2))) c) (ac+bd)/(sqrt(a^(2)+b^(2))sqrt(c^(2)+d^(2))) d) (ac-bd)/(sqrt(a^(2)+b^(2))sqrt(c^(2)+d^(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)

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

If a, b, c, d are in continued proportion, then prove that (b -c)^(2) + (c -a)^(2) + (b-d)^(2) = (a -d)^(2)