InterviewSolution
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InterviewSolution
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Let a, b, c be the sides of `Delta`ABC opposite to angles A, b,C respecitvely. Let `alpha = sum_(r=0)^(n) ""^(n)C_(r) b^(n-r) c^(r) cos{rB - (n-r)C}` and `beta = sum_(r=0)^(n) ""^(n)C_(r) b^(n-r) c^(r) sin{rB - (n-r)C}` Statement -1: `alpha = alpha^(n)` Statement-2: `beta = alpha^(n)`A. 1B. 2C. 3D. 4 |
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Answer» Correct Answer - c We have, `alpha + i beta = sum_(r=0)^(n) ""^(n)C_(r) b^(n-r) c^(r) e^(i[rB -(n-r)C])` `rArr alpha + i beta= sum_(r=0)^(n) ""^(n)C_(r) (be^(-ic))^(n-r) (ce^(iB))^%(r)` `rArr alpha + i beta= (b e ^(-iC) + ce^(iB))^(n)` `rArr alpha + i beta = {(b cos C + c cos B) + i (-b sin C + csin B)}^(n)` `rArr alpha + i beta = (a + i0)^(n)` "" `[{:(because a = b cos C + c sin B),( " "&(b)/(sinB) = (c)/(sinC)):}]` `rArr alpha + i beta = a^(n)` `rArr alpha = a^(n) and beta = 0.` |
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