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