化簡(jiǎn)：1-sin6α(六次方)-cos6(六次方）α/1-sin4(四次方）α-cos4（四次方）α

數(shù)學(xué)人氣：488 ℃時(shí)間：2019-10-23 01:31:39

優(yōu)質(zhì)解答

(1-cos^6α-sin^6α)/(1-cos^4α-sin^4α)
1=sin^2α+cos^2α
原式=(sin^2α+cos^2α-cos^6α-sin^6α) /(sin^2α+cos^2α-cos^4α-sin^4α)
分母=sin^2α(1-sin^2α)+cos^2α(1-cos^2α)=2sin^2αcos^2α
分子=sin^2α(1-sin^4α)+cos^2α(1-cos^4α)
sin^2α(1-sin^4α)=sin^2α(1-sin^2α)(1+sin^2α)=sin^2αcos^2α(1+sin^2α)
同理cos^2α(1-cos^4α)=sin^2αcos^2α(1+cos^2α)
原式=sin^2αcos^2α(1+sin^2α+1+cos^2α)/2sin^2αcos^2α=3/2