If tanA1, tan A2, tanA3 and tanA4 are the roots of the equationx^4 - x^3 sin2q + x^2 cos2q - x cosq - sinq = 0then tan(A1 + A2 + A3 + A4) is equal to(a)sinq(B)cosq(C)tanq(D)cotq

Dear Ajay

let s₁= sum of the roots taken one at a time = -(-sin2q)=sin2q

s₂=sum of the roots taken two at a time = cos2q

s₃=sum of the roots taken two at a time = -(-cosq)=cosq

s₄= sum of the roots taken four at a time = -sinq

tan(A₁+A₂+A₃+A₄)= (s₁-s₃)/(1-s₂-s₄) = (sin2q-cosq)/(1-cos2q-sinq)

= (2sinq*cosq - cosq)/(2sin²q - sinq)

=cosq(2sinq-1)/sinq(2sinq-1)

=cotq

option D

All the best.                                                           

AKASH GOYAL

AskiitiansExpert-IIT Delhi

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