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1 solution
ax^2 + bx + c = 0
Sum of roots of quadratic equation is -b/a
Product of roots of quadratic equation is c/a
Therefore, Sinθ + Cosθ = -b/a (eq1)
SinθCosθ =c/a (eq2)
(Sinθ + Cosθ)^2 = (-b/a)^2 (eq1)
(Sinθ)^2 + (Cosθ)^2 + 2SinθCosθ = b^2/a^2
1 + 2c/a = b^2/a^2
( (Sinθ)^2 + (Cosθ)^2=1) (SinθCosθ =c/a (eq2))
=a^2 + 2ac = b^2 (multiplying by a^2)
=a^2 + 2ac +c^2 = b^2 + a^2 (adding c^2 for completetion of square)
=(a+c)^2 = b^2 + c^2
Therefore, (a+c)^2/(b^2+c^2) = 1