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In triangle abc angle c is obtuse then which is correct a tanatanb 1 c none pls explain

In triangle abc angle c is obtuse then which is correct a tanatanb<1 b tanatanb>1 c none pls explain

Grade:10

1 Answers

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

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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