Question

if a b c are in ap and a = sin(b+c), b= sin(a+c), c = sin(a+b) then prove that tan a = tan b= tan c

Answer 1

you using fundamental of A.P
that is b-a=c-b
you get b=a+c/2
hence put value a,b,c
2b=a+c
2sin(a+c)=sin (b+c) +sin(a+b)
a+c=2b
2sin 2b=4sinbcosb
4 sinb cosb=sinb cosc +cosb sinc +Sina cosb +cosa sinb