In a triangle ABC, if the angle c is obtuse, then tanAtanB= 1)1 2) 3)=1 4)=0

Question

In a triangle ABC, if the angle c is obtuse, then tanAtanB= 1)>1 2) 3)=1 4)=0

Arun · Answer

Dear Sunny

In case that C is obtuse,

Then C>90.

So A+B msut be less than 90... (because in a triangle A+B+C=180, and C is above 90)

So tan(A+B) must be postivie... (Since A+B is acute

tan(A+B) = (tanA+tanB)/(1-tanAtanB)

So 1-tanAtanB>0..... (Only then tan(A+B) can be positive)

Hence tanAtanB

Hope it helps

Regards

Arun (askIITians forum expert)

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In a triangle ABC, if the angle c is obtuse, then tanAtanB= 1)>1 2) 3)=1 4)=0

In a triangle ABC, if the angle c is obtuse, then tanAtanB=
1)>1
2)
3)=1
4)=0

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In a triangle ABC, if the angle c is obtuse, then tanAtanB= 1)>1 2) 3)=1 4)=0

In a triangle ABC, if the angle c is obtuse, then tanAtanB=1)>12)3)=14)=0

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In a triangle ABC, if the angle c is obtuse, then tanAtanB=
1)>1
2)
3)=1
4)=0