Final answer:
After applying the double angle formula for tangent, the calculated result of tan(2x) was 28/45, which does not match any of the answer choices provided, indicating a possible error in the provided information or options.
Step-by-step explanation:
To find tan(2x) when given cot(x) = 7/2 in the first quadrant, we can first find tan(x) by taking the reciprocal of cot(x), which gives us tan(x) = 2/7.
Next, we use the double angle formula for tangent, which is tan(2x) = 2 tan(x) / (1 - tan2(x)). Substituting tan(x) = 2/7 into the formula, we get:
tan(2x) = (2 * (2/7)) / (1 - (2/7)2)
tan(2x) = (4/7) / (1 - 4/49)
tan(2x) = (4/7) / (49/49 - 4/49)
tan(2x) = (4/7) / (45/49)
tan(2x) = 4/7 * 49/45
tan(2x) = 196/315
After simplifying, we find that tan(2x) = 28/45. However, this result does not match any of the options provided in the question, so there might be a mistake either in the initial information given or in the options listed.