To find tan(2x) when cot(x) is 12/5 in the first quadrant, we use the double angle formula for tangent after converting cot(x) to tan(x). The computation shows that tan(2x) equals 120/119, which is not among the options provided.
The question asks us to find the value of tan(2x) given that cot(x) = 12/5 and x is in the first quadrant. To find tan(2x), we can use the double angle formula for tangent, which is tan(2x) = 2tan(x) / (1 - tan2(x)). Since cotangent is the reciprocal of tangent, we have tan(x) = 5/12. Using the formula:
- tan(2x) = 2(5/12) / (1 - (5/12)2)
- tan(2x) = 10/12 / (1 - 25/144)
- tan(2x) = 10/12 / (119/144)
- tan(2x) = (10/12) * (144/119)
- tan(2x) = 120/119
The correct answer is not listed among the options given, hence there may be an error in the given choices or the question itself.