CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If tan α, tan β are the roots of the equation x2 + ax + b = 0 then the value of sin2(α+β)+a sin(α+β)cos(α+β)+b cos2(α+β)=


A

a

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

b

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C

ab

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

1a+b

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B

b


tan α+tan β=a, tan α tan β=btan (α+β)=tan α+tan β1tan α tan βtan (α+β)=a1b=ab1
Now sin2(α+β)+a sin (α+β)cos(α+β)+b cos2(α+β)=cos2(α+β)[tan2(α+β)+a tan(α+β)+b]=tan2(α+β)+a tan(α+β)+bsec2(α+β)=tan2(α+β)+a tan (α+β)+b1+tan2(α+β)
=a2(b1)2+a.ab1+b1+a2(b1)2=ab1(ab1+a)+b1+a2(b1)2=ab1(a+abab1)+b1+a2(b1)2=b


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Relation of Roots and Coefficients
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon