Correct option (B) x = nπ, n∈Z
We have tan 3x = tan 5x. So
5x = nπ + 3x ,n ∈ Z ⇒ x = nπ/2, n ∈Z
If n is odd, then x = nπ/2 gives the extraneous solutions. Thus, the solution of the given equation can not given by x = nπ/2, where n is even say n = 2 m, m∈Z. Hence, the required solution is x = nπ, n ∈ Z.
