If-are-the-roots-of-the-equation-ax-2-bx-c-0-then-the-value-of-the-determinant-determinant-1-cos-cos-cos-1-cos-cos-cos-1-is-

Question Number 41820 by v tfvhjdxf last updated on 13/Aug/18

If α, β are the roots of the equation

{a x}^{2} + b x + c = 0, then the value of the

determinant

| \begin{matrix} 1 & \cos (β - α) & \cos α \\ \cos (α - β) & 1 & \cos β \\ \cos α & \cos β & 1 \end{matrix} | is

Answered by tanmay.chaudhury50@gmail.com last updated on 15/Aug/18

1 (1 - {c o s}^{2} β) - c o s (β - α) {c o s (α - β) - c o s α c o s β} + c o s α {c o s (α - β) c o s β - c o s α}

{s i n}^{2} β - c o s (β - α) (s i n α s i n β) + c o s α c o s β c o s (α - β) - {c o s}^{2} α

{s i n}^{2} β - {c o s}^{2} α + c o s (α - β) {c o s α c o s β - s i n α s i n β)

{s i n}^{2} β - {c o s}^{2} α + c o s (α - β) c o s (α + β)

\frac{1}{2} (2 {s i n}^{2} β - 2 {c o s}^{2} α + c o s 2 α + c o s 2 β)

\frac{1}{2} (2 {s i n}^{2} β - 2 {c o s}^{2} α + 2 {c o s}^{2} α - 1 + 1 - 2 {s i n}^{2} β)

\frac{1}{2 (} \times 0 = 0

p l s c h e c k