If a, b, c are sides of a triangle and a3, b3, c3 are roots of x3−px2+qx−r=0, then match the following list - I with list - II List - IList - II(P)sin3 A+sin3 B+sin3 C−3 sin A sin B sin C=8D31.p=14,q=5, r=8(Q)a sin2 A+b sin2 B+c sin2 C=14D22.p=36,q=7, r=2(R)sin A sin B sin C=2D33.p=9,q=7, r=8(S)a cos2 A+b cos2 B+c cos 2C=2(S−Δ2)4.p=632, q=5, r=275.p=1, q=8, r=8 (here Δ denotes area of triangle and S represents semi perimeter)

If a, b, c are sides of a triangle and a3, b3, c3 are roots of x3−px

1.	If a, b, c are sides of a triangle and a3, b3, c3 are roots of x3−px2+qx−r=0, then match the following list - I with list - II List - IList - II(P)sin3 A+sin3 B+sin3 C−3 sin A sin B sin C=8D31.p=14,q=5, r=8(Q)a sin2 A+b sin2 B+c sin2 C=14D22.p=36,q=7, r=2(R)sin A sin B sin C=2D33.p=9,q=7, r=8(S)a cos2 A+b cos2 B+c cos 2C=2(S−Δ2)4.p=632, q=5, r=275.p=1, q=8, r=8 (here Δ denotes area of triangle and S represents semi perimeter)
Answer» If a, b, c are sides of a triangle and $a^{3}, b^{3}, c^{3}$ are roots of $x^{3} - p x^{2} + q x - r = 0$ , then match the following list - I with list - II $\begin{matrix} List - I & List - II (P) & s i n^{3} A + s i n^{3} B + s i n^{3} C - 3 s i n A s i n B s i n C = 8 D^{3} & 1. & p = 14, q = 5, r = 8 (Q) & a s i n^{2} A + b s i n^{2} B + c s i n^{2} C = 14 D^{2} & 2. & p = 36, q = 7, r = 2 (R) & s i n A s i n B s i n C = 2 D^{3} & 3. & p = 9, q = 7, r = 8 (S) & a c o s^{2} A + b c o s^{2} B + c c o s 2 C = 2 (S - Δ^{2}) & 4. & p = \frac{63}{2}, q = 5, r = 27 5. & p = 1, q = 8, r = 8 \end{matrix}$ (here $Δ$ denotes area of triangle and S represents semi perimeter)