If in a △ABC, 4 tanA+3=0 then sinA2 and cosA2 are the roots of
tanA=−34.
Hence
sinA=−35 and cosA=45.
Then
cosA2=√1+cosA2
=√910
=3√10 ...(i)
And
sin(A2)=√1−cosA2
=1√10.
Hence
Sum of roots =4√10
And
Product of roots =310.
Hence the correct answer is option A.