Final answer:
When solving cot x cos^2 x = 2 cot x, you can divide each side by cot x if cot x is not equal to 0, simplifying the equation to cos^2 x = 2, but remember to consider angles where cot x is undefined.
Step-by-step explanation:
When solving the trigonometric equation cot x cos2 x = 2 cot x, dividing each side by cot x is a valid step provided that cot x is not equal to 0. To simplify the equation, we can cancel out the cot x terms, which will leave us with cos2 x = 2. However, one must be careful to consider the values of x where cot x is undefined before dividing. These values correspond to the angles where cosine is 0, or in other words, the multiples of π/2 (90 degrees), which should be excluded as solutions if they are part of the initial equation's domain.