( sin^3(x) + cos^3(x) ) / ( sin^2(x) - cos^2(x) ) Please help me simplify this one. Giving me a headache.

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- Dec 14th 2009, 01:29 PMFaRmBoXHelp Simplifying
( sin^3(x) + cos^3(x) ) / ( sin^2(x) - cos^2(x) ) Please help me simplify this one. Giving me a headache.

- Dec 14th 2009, 01:35 PMe^(i*pi)
- Dec 14th 2009, 01:44 PMFaRmBoX
That was my bad, it the first value divided by the 2nd value. I put them one above the other as I typed it and I didnt realize the entire post ended being one line. ( sin^3(x) + cos^3(x) ) / ( sin^2(x) - cos^2(x) )

- Dec 14th 2009, 01:54 PMe^(i*pi)

Slightly different this time. Again use the sum of two cubes on the top

As we get

As far as I know once goes it cannot be reduced further

This time use the difference of two squares on the bottom to ensure something will cancel in the step after this

Bring both parts together