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In triangle abc angle c is obtuse then which is correct a. tana.tanb <1 b. tana.tanb>1 c. none
Hi Rishab,
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 < 90)
tan(A+B) = (tanA+tanB)/(1-tanAtanB)
So 1-tanAtanB>0..... (Only then tan(A+B) can be positive)
Hence tanAtanB<1
Option (A) would be the answer.
Best Regards,
Ashwin (IIT Madras).
as a+b<90
tan(a+b)<tan90
tana+tanb/1-tana*tanb<infinity
1-tana*tanb>0
tana*tanb<1
so the option is a
In given situation angle c is pbtuse that means rest two angles a and b are acute (bcoz sum of trio of angles in a tringle=180)
finding tana = 1/tanb(by figure where c is obtuse angle at middle)
i.e. tana.tanb=1
so the answer is c. none.
plz approve my answer if u like
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