化简1-cos4α-sin4α/1-cos5α-sin6α（数字是次数,如图所示）

化简(1-cos⁴α-sin⁴α)/(1-cos⁵α-sin⁶α)
原式=[1-(cos⁴α+sin⁴α)]/[1-cos⁵α-(1-cos²α)³]
=[1-(cos²α+sin²α)²+2sin²αcos²α]/[1-cos⁵α-(1-3cos²α+3cos⁴α-cos⁶α)]
=(2sin²αcos²α)/(cos⁶α-cos⁵α-3cos⁴α+3cos²α)
=(2sin²α)/(cos⁴α-cos³α-3cos²α+3)
=(2sin²α)/[(cosα-1)(cos³α-3cosα-3)]
=[2(1-cos²α)]/[(cosα-1)(cos³α-3cosα-3)]
=[-2(cosα+1)(cosα-1)]/[(cosα-1)(cos³α-3cosα-3)]
=-2(cosα+1)/(cos³α-3cosα-3)