SOLUTION: How do you prove that {{{cos(5x) = 5 cos(x) - 20 cos^3(x) + 16 cos^5(x)}}} using sum and difference identities? Thank you :D *EDIT: I'm so sorry, cos^5 x should be cos 5x

Algebra ->  Trigonometry-basics -> SOLUTION: How do you prove that {{{cos(5x) = 5 cos(x) - 20 cos^3(x) + 16 cos^5(x)}}} using sum and difference identities? Thank you :D *EDIT: I'm so sorry, cos^5 x should be cos 5x      Log On


   



Question 604252: How do you prove that cos%285x%29+=+5+cos%28x%29+-+20+cos%5E3%28x%29+%2B+16+cos%5E5%28x%29 using sum and difference identities? Thank you :D
*EDIT: I'm so sorry, cos^5 x should be cos 5x

Found 2 solutions by jsmallt9, jjvseg:
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
This cannot be correct because ...
  • What you posted was:
    cos%5E5%28x%29+=+5cos%28x%29+-+20cos%5E3%28x%29+%2B+16cos%5E5%28x%29
    This is not an identity. This equation is only true for certain values of x, not all values of x.; and
  • All the arguments are x. There is no need to use sum and/or difference identities to manipulate the arguments.

If you re-post the question, then I wonder if the double angle and half angle identities would be considered "sum and difference identities"? I ask because I suspect that they might be very helpful.

Answer by jjvseg(1) About Me  (Show Source):