To find the general solution of the equation cot(x) + tan(x) = 2 csc(x), we can rewrite the equation in terms of sine and cosine.

Recall that cot(x) = cos(x)/sin(x), tan(x) = sin(x)/cos(x), and csc(x) = 1/sin(x). Substituting these into the equation, we get:

cos(x)/sin(x) + sin(x)/cos(x) = 2/sin(x)

Multiplying both sides by sin(x)cos(x) to clear the fractions, we obtain:

cos²(x) + sin²(x) = 2cos(x)

Since cos²(x) + sin²(x) = 1, the equation simplifies to:

1 = 2cos(x)

cos(x) = 1/2

The general solution for cos(x) = 1/2 is given by:

x = 2πn ± π/3, where n is an integer.

We need to check for extraneous solutions. The original equation involves cot(x), tan(x), and csc(x), so we must ensure that sin(x) ≠ 0 and cos(x) ≠ 0.

sin(x) ≠ 0 when x ≠ nπ, where n is an integer.

cos(x) ≠ 0 when x ≠ (2n+1)π/2, where n is an integer.

The solutions x = 2πn ± π/3 do not violate these conditions. Therefore, the general solution is:

x = 2πn + π/3 or x = 2πn - π/3, where n is an integer.