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Q.

If A, B, C are the angles of a triangle such that angle A is obtuse then

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a

tan⁡Atan⁡B<1

b

tan⁡Btan⁡C<1

c

tan⁡Ctan⁡A<1

d

tan⁡Atan⁡Btan⁡C<1

answer is B.

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Detailed Solution

A>π/2 B+C<π/2⇒tan⁡(B+C)>0⇒ tan⁡B+tan⁡C1−tan⁡Btan⁡C>0⇒ tan⁡Btan⁡C<1( as tan⁡B,tan⁡C>0)
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