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Ajay Kumar Grade: 11
        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
6 years ago

Answers : (1)

AKASH GOYAL AskiitiansExpert-IITD
419 Points
										

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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6 years ago
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