document.write( "Question 633784: Verify the identity.
\n" ); document.write( "csc^4theta - csc^2theta = cot^4theta + cot^2theta \n" ); document.write( "

Algebra.Com's Answer #399257 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"csc%5E4%28theta%29+-+csc%5E2%28theta%29+=+cot%5E4%28theta%29+%2B+cot%5E2%28theta%29\"$
\n" ); document.write( "There's two keys to this:

A 4th power is the same as squared squared. So $\"csc%5E4%28theta%29+=+%28csc%5E2%28theta%29%29%5E2\"$ ; and
There is an identity that connects csc squared and cot squared: $\"csc%5E2%28x%29+=+cot%5E2%28x%29+%2B+1\"$

Once you recognize these two facts, this is a farily simple problem.

\n" ); document.write( "1. Rewrite the left side in terms of csc squared:
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\n" ); document.write( "2. Replace the csc squared's with cot squared plus one:
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\n" ); document.write( "3. Simplify. I'll leave this part up to you with these hints:

Use FOIL or the $\"%28a%2Bb%29%5E2+=+a%5E2%2B2ab%2Bb%5E2\"$ pattern to multiply out $\"%28cot%5E2%28theta%29%2B1%29%5E2\"$ .
Combine like terms while being careful to notice the minus in front of $\"%28cot%5E2%28theta%29%2B1%29\"$ .

\n" ); document.write( "If you do this correctly the left side matches the right side fairly quickly. \n" ); document.write( "

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