SOLUTION: I need to prove that (2sinx+3cosx)^2 + (3sinx-2cosx)^2 = 13 work would be appreciated. thank you

Algebra ->  Trigonometry-basics -> SOLUTION: I need to prove that (2sinx+3cosx)^2 + (3sinx-2cosx)^2 = 13 work would be appreciated. thank you      Log On


   

Question 427300: I need to prove that
(2sinx+3cosx)^2 + (3sinx-2cosx)^2 = 13
work would be appreciated. thank you
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Expand the left side:



The 12+sin%28x%29cos%28x%29 terms cancel out, leaving

4sin%5E2%28x%29+%2B+9+cos%5E2%28x%29+%2B+9sin%5E2%28x%29+%2B+4cos%5E2%28x%29

Collect like terms to obtain

13sin%5E2%28x%29+%2B+13cos%5E2%28x%29+=+13%28sin%5E2%28x%29+%2B+cos%5E2%28x%29%29. Since sin%5E2%28x%29+%2B+cos%5E2%28x%29+=+1 we conclude that the entire expression is equal to 13.