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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