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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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