Question

If  x, y, z are in AP and tan^-1x,tan^-1y and tan^-1 z are also in AP, then

(A)  x = y = z

(B)  x = y = -z

(C)  x = 1; y = 2; z = 3

(D)  x = 2; y = 4; z = 6

Answer 1

Correct option (A)  x = y = z

But 2y =  x + z . Therefore,

1 - y² = 1 - xz ⇒ y² = Xz

Since, x, y, z are both in GP and AP, therefore,

x = y = z