In a triangle ABC we knw that
tan A + tan B + tan C = tan A tanB tan C
now using AP> GP
thrfore tan C + tan B > 2 sqrrt(tan B tan C)
using the first equation, we have
tan A tanB tan C - tan A > 2 sqrrt(tan B tan C)
=> tan A (tanB tan C -1) > 2 sqrrt(tanB tan C)
now we have tan A < 0....as A is obtuse, and RHS >0....
thrfore tanB tan C -1 <0
=> tanB tan C < 1
so the first option is correct!!!!!!
Moderation Team
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