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
To simplify the expression (1+)/()( - ), we will follow these steps: Step 1: Rewrite and in terms of and . Recall the definitions: = (1)/() = ()/() Step 2: Substitute these into the expression. (1+)/()((1)/() - ()/()) Step 3: Simplify the term inside the parenthesis by finding a common denominator. (1)/() - ()/() = (1-)/() Step 4: Substitute this simplified term back into the main expression. (1+)/()((1-)/()) Step 5: Multiply the numerators and the denominators. ((1+)(1-))/( · ) Step 6: Simplify the numerator using the difference of squares formula, (a+b)(a-b) = a^2 - b^2. Here, a=1 and b=. (1+)(1-) = 1^2 - ^2 = 1 - ^2 Step 7: Apply the Pythagorean identity ^2 + ^2 = 1. From this identity, we know that 1 - ^2 = ^2. So, the numerator becomes ^2. Step 8: Simplify the denominator. · = ^2 Step 9: Substitute the simplified numerator and denominator back into the expression. (^2)/(^2) Step 10: Simplify the fraction. Assuming ^2 ≠ 0, the expression simplifies to 1. The final answer is B. 1.