This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions. 1. Given (A) = 5/13 and (B) = 3/5, where A and B are acute angles, find (A+B). Step 1: Find (A) and (B). Since A is acute, (A) = sqrt(1-^2(A)) = sqrt(1-((5)/(13))^2) = sqrt(1-(25)/(169)) = sqrt((144)/(169)) = (12)/(13). Since B is acute, (B) = sqrt(1-^2(B)) = sqrt(1-((3)/(5))^2) = sqrt(1-(9)/(25)) = sqrt((16)/(25)) = (4)/(5). Step 2: Apply the sum formula for sine. (A+B) = (A)(B) + (A)(B) = ((5)/(13))((3)/(5)) + ((12)/(13))((4)/(5)) = (15)/(65) + (48)/(65) = (15+48)/(65) = (63)/(65) The final answer is (63)/(65). 2. Given (A) = 1/3 and (B) = 1/4, find (A+B). Step 1: Apply the sum formula for tangent. (A+B) = ((A)+(B))/(1-(A)(B)) = (1)/(3)+(1)/(4)1-((1)/(3))((1)/(4)) = (4)/(12)+(3)/(12)1-(1)/(12) = (7)/(12)(12)/(12)-(1)/(12) = (7)/(12)(11)/(12) = (7)/(11) The final answer is (7)/(11).