Final answer:
Using the given value tan(A/2) = 5/12 and the double angle formula for tangent, we find tanA = 12/5. Employing the Pythagorean identity, we calculate sinA = 12/13 and cosA = 5/13. The correct trigonometric values for A are therefore sinA = 12/13, cosA = 5/13, and tanA = 12/5.
Step-by-step explanation:
To find the value of sinA, cosA, and tanA given that tan(A/2) = 5/12, we can employ trigonometric identities. We can start by expressing tan(A/2) in terms of sinA and cosA using the double angle formulas, specifically the tangent double angle formula which states that tanA = 2tan(A/2)/(1 - tan^2(A/2)). Using the given value of tan(A/2), we can find:
tanA = 2*(5/12)/(1 - (5/12)^2) = 10/12 / (1 - 25/144) = 120/144 / 119/144 = 120/119 = 12/5
The next step is to use the Pythagorean identity which relates sinA, cosA, and tanA. Since sin^2A + cos^2A = 1, and tanA is sinA/cosA, we can find sinA and cosA knowing tanA. As we've found tanA = 12/5 and it equals sinA/cosA, assuming cosA is positive, sinA would then be 12/13 and cosA would be 5/13. Therefore, the correct values are:
- sinA = 12/13
- cosA = 5/13
- tanA = 12/5
The correct option is C) sinA = 12/13, cosA = 5/13, tanA = 12/5.