Final answer:
The value of tan(2x), given tan(x) = 21/20, is found by applying the double-angle formula for tangent and simplifying the result, arriving at 420/399 (option c).
Step-by-step explanation:
The student asks about finding the value of tan(2x) given that tan(x) = 21/20. To solve this problem, we can use the double-angle formula for tangent, which is tan(2x) = 2tan(x) / (1 - tan2(x)). Substituting the given value into the formula, we get:
- tan(2x) = 2(21/20) / (1 - (21/20)2)
- tan(2x) = 42/20 / (1 - 441/400)
- tan(2x) = 42/20 / (400/400 - 441/400)
- tan(2x) = 42/20 / (-41/400)
- tan(2x) = (42/20) * (400/(-41))
- tan(2x) = 42 * 20 / 41
- tan(2x) = 840/41
- tan(2x) = 420/399 when simplified
The correct answer from the given options is therefore (c) 420/399.