SOLUTION: Can you also help me with the expression cos^2 theta -cos 2 theta is equivalent to

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Question 617165: Can you also help me with the expression cos^2 theta -cos 2 theta is equivalent to
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
cos%5E2%28theta%29-cos%282theta%29
There are three variations of the cos%282theta%29 formula:
  • cos%282theta%29+=+cos%5E2%28theta%29-sin%5E2%28theta%29
  • cos%282theta%29+=+2cos%5E2%28theta%29-1
  • cos%282theta%29+=+1-2sin%5E2%28theta%29
Any of them can be used. I'm choosing the first one because I see the rest being slightly faster/easier by choosing it:
cos%5E2%28theta%29-%28cos%5E2%28theta%29-sin%5E2%28theta%29%29
Note the use of parentheses! It is very important to use them when substituting in a multiple-term expression. Here it helps us see that the sin%5E2%28theta%29 is supposed to get subtracted, too. The cos%5E2%28theta%29's cancel and the subtraction of -sin%5E2%28theta%29 leaves us with:
sin%5E2%28theta%29