if a,b,c are angles of triangle such that a is obtuse, Then show that TanBTanC <1 Question if a,b,c are angles of triangle such that a is obtuse, Then show that TanBTanC <1 in progress 0 Math Savannah 9 months 2021-08-20T16:01:28+00:00 2021-08-20T16:01:28+00:00 1 Answer 0 views 0

## Answers ( )

It has given that a, b, c are angles of a triangle such that a is obtuse angle.

: Tanb . tanc < 1To show that: as it has given that a is obtuse anglesolutionso, π/2 < a < π

⇒π/2 < π – (b + c) < π. [ because a + b + c = π ]

⇒π/2 – π < -(b + c) < π – π

⇒-π/2 < -(b + c) < 0

⇒0 < (b + c) < π/2

⇒(b + c) < π/2

⇒b < π/2 – c

⇒tanb < tan(π/2 – c)

⇒tanb < cotc

⇒tanb < 1/tanc [ assuming value of tanc > 1]

⇒tanb tanc < 1

hence proved .