Grade 11Trigonometry
if a,b are the roots of a tan 2 theta + b sec 2 theta =c prove that tan a .tan b =b-c/b+c
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f a,b are the roots of a tan 2 theta + b sec 2 theta =c prove that tan a .tan b =b-c/b+c
1 Answer
Utsav Basu
α and β are roots of atan2 θ + bsec2 θ – c = 0
Now,
atan2 θ + bsec2 θ – c = 0
or, atan2 θ + b(1 + tan2 θ) – c = 0
or, (a + b) tan2 θ + (b – c) = 0
Thus, tan α * tan β = (b – c)/(a + b)
I am sorry, but this is the correct answer. I suppose your question is wrong.
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