SOLUTION: <pre>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 - x

Algebra ->  Test -> SOLUTION: <pre>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 - x      Log On


   

Question 1152225: 
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   |
Answer by Edwin McCravy(20081) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = x + x²
Let b = x - x²

 

Expand 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 

sin%282x%5E%22%22%29cos%282x%5E2%29%5E%22%22%2B%0D%0Acos%282x%29sin%282x%5E2%29%5E%22%22

Using identity for sin(a + b),

sin%282x%2B2x%5E2%29

Edwin