IIT JEE , AIEEE Forum - Mathematics , Trignometry

Sree

If atan A+btanB=(a+b)tan((A+B)/2) then

a)

is isoceles.

b)

is equilateral.

c)

is right.

d)none of these.

calculas

the ans is definitely equilateral triangle

puneet

hiiiii

Well this is a easy one ...

just take terms of a on one side and those with b on other ..

a ( tanA - tan((A+B)/2) ) = b ( tan((A+B)/2) - tanB )

or, [a.sin((A-B)/2)]/cosA.cos((A+B)/2) = [b.sin((A-B)/2)]/cosB.cos((A+B)/2)

or, sin((A-B)/2).[a/cosA - b/cosB] = 0

or, sin((A-B)/2).[k.sinA/cosA - k.sinB/cosB] = 0

or, sin((A-B)/2).[tanA - tanB] = 0

so, definitely A = B

and hence the triangle is isoceles.

cheers