CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
Question


If tanα,tanβ are the roots of the equation x2+px+q=0(p0) then
sin2(α+β)+psin(α+β)cos(α+β)+qcos2(α+β)=

A
0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
p
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
q
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D q

x2+px+q=0
tanα+tanβ=p
tanαtanβ=q
tan(α+β)=p1q=pq1
sin2(α+β)+psin(α+β)cos(α+β)+qcos2(α+β)
cos2(α+β)[tan2(α+β)+ptan(α+β)+q]
=[p2(q1)2+p2q1+1]cos2(α+β)
=[p2+p2qp2+q(q22p+1)(q1)2]cos2(α+β)
=[p2q+q32pq+q(q1)2]cos2(α+β)
=q(p2+q22p+1)(q1)2(q1)2(p2+q22q+1)
=q


flag
Suggest Corrections
thumbs-up
0
mid-banner-image
mid-banner-image
similar_icon
Related Videos
thumbnail
lock
Relation of Roots and Coefficients
MATHEMATICS
Watch in App