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 prove the identity ^4 + ^2 = ^4 - ^2 . Step 1: Start with the Left Hand Side (LHS) of the equation. LHS = ^4 + ^2 Step 2: Factor out ^2 from the expression. LHS = ^2 (^2 + 1) Step 3: Use the trigonometric identity 1 + ^2 = ^2 . Substitute this into the expression. LHS = ^2 (^2 ) Step 4: Use the same identity to express ^2 in terms of ^2 , which is ^2 = ^2 - 1. Substitute this into the expression. LHS = (^2 - 1) (^2 ) Step 5: Distribute ^2 across the terms in the parenthesis. LHS = ^2 · ^2 - 1 · ^2 LHS = ^4 - ^2 Step 6: Compare the result with the Right Hand Side (RHS) of the original equation. RHS = ^4 - ^2 Since LHS = RHS, the identity is proven. ^4 + ^2 = ^4 - ^2