Using the properties of determinants and trigonometry identities, show that
|cos(x + x²) sin(x + x²) -cos(x + x²)|
|A| = |sin(x - x²) cos(x - x²) sin(x - x²)| = sin(2x + 2x²)
| sin2x 0 sin2x² |Let a = x + x² Let b = x - x²Expand about the bottom row: Swap the terms in the first big parentheses so you'll recognize the identity: Using identities for cos(a ± b) Swapping the factors in the second term so you'll recognize the identity: Since a = x + x² andb = x - x², a+b = 2x and a-b = 2x² Using identity for sin(a + b), Edwin