Question

If A, B, C
angles of a triangle such that
A is obtuse, then tanB. tanC=​

Answer 1

Step-by-step explanation:

A is obtuse angle.

Then

2

π

<A<π

⇒

2

π

<π−(B+C)<π

⇒−

2

π

>−π+(B+C)>−π

⇒

2

π

>(B+C)>0

∵B+C<

2

π

⇒B<

2

π

−C

⇒tanB<tan(

2

π

−C)

⇒tanB<cotC

∴tanB<

tanC

1

Hence tanBtanC<1