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
You're on a roll — Step 1: Start with the left-hand side (LHS) of the identity. The LHS is ()/(1-). Step 2: Multiply the numerator and denominator by the conjugate of the denominator, which is 1+. ()/(1-) = ()/(1-) × (1+)/(1+) = ((1+))/((1-)(1+)) Step 3: Expand the numerator and use the difference of squares formula (a-b)(a+b) = a^2-b^2 in the denominator. = ( + )/(1^2 - ^2) = ( + )/(1 - ^2) Step 4: Apply the Pythagorean identity ^2 + ^2 = 1, which means 1 - ^2 = ^2. = ( + )/(^2) Step 5: Separate the fraction into two terms. = ()/(^2) + ()/(^2) Step 6: Simplify each term. = (1)/() + ()/() Step 7: Express the terms using and . We know that (1)/() = and ()/() = . = + This is equal to the right-hand side (RHS) of the identity. Thus, ()/(1-) = + is proven. Drop the next question.