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.
To show that : Tanb . tanc < 1
solution : as it has given that a is obtuse angle
so, 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 .