Final answer:
To solve tan(2x) = 0, we look for angles where tangent is zero, which are integer multiples of π. Therefore, 2x = nπ, and dividing by 2 gives us x = nπ/2, which includes all integer multiples of π/2 radians.
Step-by-step explanation:
To solve tan(2x) = 0 using the double angle formula, we first need to understand the properties of the tangent function. A tangent of an angle equals zero whenever its associated angle is an integer multiple of π. The double angle formula for tangent is tan(2x) = 2tan(x) / (1 - tan^2(x)), but since tan(2x) = 0, we don't need the formula in this case as we are looking for the angles where the tangent is zero.
Therefore, 2x must be equal to nπ, where n is an integer. We can solve for x simply by dividing by 2: x = nπ/2. Thus, the general solution for x is any integer multiple of π/2 radians, which corresponds to 0, π/2, π, 3π/2, 2π, etc., considering both positive and negative multiples.