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If tanA and tanB are roots of x^2 - 2x-1=0, then sin^2(A+B) is

If tanA and tanB are roots of x^2 - 2x-1=0, then sin^2(A+B) is

Grade:11

1 Answers

Arun
25750 Points
3 years ago
Given,
 
x2−2x−1=0
 
x=2⋅1−(−2)±(−2)2−4⋅1(−1)​​
 
x=1+2​,x=1−2​
 
⇒tanA=1+2​,tanB=1−2​
 
⇒A=tan−1(1+2​),B=tan−1(1−2​)
 
⇒A=6721​∘,B=2221​∘
 
Now,
 
sin2(A+B)
 
=sin2(6721​∘+2221​∘)
 
=sin2(90∘)
 
=1

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