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
Welcome back Nontokozo — been a while! Let's pick up where you left off. To prove the identity, we will start with the left-hand side (LHS) and transform it into the right-hand side (RHS). The identity to prove is: (2 x - 2 x x)/(2 ^2 x) = x Step 1: Start with the Left Hand Side (LHS) and express x in terms of x and x. LHS = (2 ( x)/( x)) - 2 x x2 ^2 x Step 2: Find a common denominator for the terms in the numerator. LHS = (2 x)/( x) - (2 x x · x)/( x)2 ^2 x LHS = (2 x - 2 x ^2 x)/( x)2 ^2 x Step 3: Factor out 2 x from the numerator. LHS = (2 x (1 - ^2 x))/( x)2 ^2 x Step 4: Apply the Pythagorean identity 1 - ^2 x = ^2 x. LHS = (2 x (^2 x))/( x)2 ^2 x LHS = (2 ^3 x)/( x)2 ^2 x Step 5: Simplify the complex fraction by multiplying the numerator by the reciprocal of the denominator. LHS = (2 ^3 x)/( x) · (1)/(2 ^2 x) Step 6: Cancel out common terms (2 and ^2 x). LHS = (^3 x)/(^2 x x) LHS = ( x)/( x) Step 7: Recognize that ( x)/( x) = x. LHS = x Since LHS = RHS, the identity is proven. The identity is proven. Send me the next one 📸