Question

pls answer this question ​

Answer 1

Answer:

Option(2)

Step-by-step explanation:

Given angle C is obtuse. { C > 90}

So, A + B must be less than 90.

A + B < 90

Then:

⇒ tan(A + B) < tan90

⇒ tanA+tanB/1 - tanAtanB < ∞

⇒ 1 - tanAtanB > 0

⇒ tanA*tanB < 1

Hope it helps!

Answer 2

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