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:- A 4th power is the same as squared squared. So ; and
- There is an identity that connects csc squared and cot squared:
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:- Use FOIL or the pattern to multiply out .
- 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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