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 — The double angle identity 2x = 2^2 x - 1 is derived from the cosine addition formula and the Pythagorean identity. Step 1: Start with the cosine addition formula. (A+B) = A B - A B Step 2: Let A=x and B=x. (x+x) = x x - x x 2x = ^2 x - ^2 x Step 3: Use the Pythagorean identity ^2 x + ^2 x = 1, which means ^2 x = 1 - ^2 x. Substitute this into the equation from Step 2: 2x = ^2 x - (1 - ^2 x) Step 4: Simplify the expression. 2x = ^2 x - 1 + ^2 x 2x = 2^2 x - 1 This shows how the identity 2x = 2^2 x - 1 is derived. Got more? Send 'em!