Q: If ABC is a triangle such that angle A is obtuse, then
(A) tan B tan C > 1
(B) tan B tan C < 1
(C) tan B tan C = 1
(D) none of these
Sol. tan A = – tan (B + C)
⇒ $\large tanA = \frac{tanB + tanC}{tanB tanC – 1}$
Since A is obtuse
∴ tan B tan C – 1 < 0
⇒ tan B tan C < 1
Hence (B) is the correct answer.
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