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Hi Rishab,
As angle C is obtuse, we have C>90
So A+B = 180 - C
So A+B<90
And hence tan(A+B) must be positive. Since tan(acute angle), is positive.
And also tan(A+B)= [tanA+tanB]/(1-tanAtanB)
Now, tan(A+B) is positive, tanA is positive, tanB is positive. So (1-tanAtanB should be positive)....
Hence 1-tanAtanB>0.... or tanAtanB<1
Option (A), is correct.
Best Regards,
Ashwin (IIT Madras).
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