Question

If the non zero numbers x, y, z are in A.P. and tan^–1x, tan^–1y, tan^–1z are also in A.P. then –

• A. x = y = z
• B. xy = yz
• C. x² = yz
• D. z² = xy

Answer 1

Answer: (A)

x = y = z

Answer 2

2y = x + z ......(1) (Q x, y, z are in A.P.)

Also, 2 tan^–1y = tan^–1x + tan^–1z

tan^–1 = tan^–1 $\left( \frac { \mathrm { X } + \mathrm { Z } } { 1 - \mathrm { XZ } } \right)$ ̃1 – y² = 1– xz

or x,y,z are in G.P. \ x = y = z