SOLUTION: Verify the identity. csc^4theta - csc^2theta = cot^4theta + cot^2theta

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Question 633784: Verify the identity.
csc^4theta - csc^2theta = cot^4theta + cot^2theta

Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!

There's two keys to this:Once you recognize these two facts, this is a farily simple problem.

1. Rewrite the left side in terms of csc squared:

2. Replace the csc squared's with cot squared plus one:

3. Simplify. I'll leave this part up to you with these hints:
  1. Use FOIL or the pattern to multiply out .
  2. Combine like terms while being careful to notice the minus in front of .

If you do this correctly the left side matches the right side fairly quickly.

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