Question

prove that (a+b)^2 / 4ab = sin^2 x is only possible only when a = b

Answer 1

(a+b) = sqrt(a^2+b^2+2ab)

(a-b) = sqrt(a^2+b^2-2ab)

Let x = (a+b)/(a-b)

=> x^2 = (a^2+b^2+2ab)/(a^2+b^2-2ab)

=> x^2 = (4ab+2ab)/(4ab-2ab)

=> x^2 = 3

=> x = sqrt(3).

(a+b)/(a-b)= sqrt(3)