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If tanA1, tan A2, tanA3 and tanA4 are the roots of the equation x^4 - x^3 sin2q + x^2 cos2q - x cosq - sinq = 0 then 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 Please feel free to post as many doubts on our discussion forum as you can. We are all IITians and here to help you in your IIT JEE preparation. Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian. Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar respectively : Click here to download the toolbar..
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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