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Find the cot sum

Source: Baltic Way 1996 Q14

March 19, 2011
functionalgebra proposedalgebra

Problem Statement

The graph of the function f(x)=xn+an−1xn−1+…+a1x+a0f(x)=x^n+a_{n-1}x_{n-1}+\ldots +a_1x+a_0 (where n>1n>1) intersects the line y=by=b at the points B1,B2,…,BnB_1,B_2,\ldots ,B_n (from left to right), and the line y=c (c≠b)y=c\ (c\not= b) at the points C1,C2,…,CnC_1,C_2,\ldots ,C_n (from left to right). Let PP be a point on the line y=cy=c, to the right to the point CnC_n. Find the sum cot⁡(∠B1C1P)+…+cot⁡(∠BnCnP)\cot (\angle B_1C_1P)+\ldots +\cot (\angle B_nC_nP)
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