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 is the solution for number 10. 10. Find the exact value of (15^). Step 1: Express 15^ as a difference of standard angles. (15^) = (45^ - 30^) Step 2: Apply the tangent difference formula (A-B) = ((A)-(B))/(1+(A)(B)). = ((45^) - (30^))/(1 + (45^)(30^)) = (1 - 1)/(sqrt(3))1 + 1 · (1)/(sqrt(3)) Step 3: Simplify the expression. = sqrt(3)-1sqrt(3)sqrt(3)+1sqrt(3) = sqrt(3)-1sqrt(3)+1 Step 4: Rationalize the denominator. = sqrt(3)-1sqrt(3)+1 · sqrt(3)-1sqrt(3)-1 = (sqrt(3))^2 - 2sqrt(3) + 1^2(sqrt(3))^2 - 1^2 = 3 - 2sqrt(3) + 13 - 1 = 4 - 2sqrt(3)2 = 2 - sqrt(3) The final answer is 2 - sqrt(3).