Given that sin x + i cos 2x and cos x – i sin 2x are conjugate to each other.
⇒ sin x - i cos 2x = cos x – i sin 2x
On comparing real and imaginary parts of both sides, we get
⇒ sin x = cos x and cos 2x = sin 2x
⇒ tan x = 1 and tan 2x = 1
Consider tan 2x = 1
This is not satisfied by tan x = 1.
Hence, no value of x is possible.