Question

x, y, z are in Arithmetic progression also tan^−1x, tan^-1y, tan^-1z are also in AP. Can you prove -a, 0, a is the solution for x, y, z and 'a' being any real number.​

Answer 1

Answer:

since arctanx,arctany and arctanz are in AP

2(tan^-1y)=tan^-1x + tan^-1z

tan^-1(2y/1-y^2) = tan^-1(x+z/1-xz)

applying tan on both sides we get

2y/1-y^2 = x+z/1-xz

now given -a,0,a is solution for x,y,z a€R

LHS =0 as y=0

implies 0=x+z

x=-z. ( therefore -a,0,a)