Grade 11IIT JEE Entrance Exam
If tanA and tanB are roots of x^2 - 2x-1=0, then sin^2(A+B) is
1 Answer
Arun
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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