In triangle abc angle c is obtuse then which is correcta tanatanb1c nonepls explain

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).