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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```
6 years ago

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

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```
6 years ago
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