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

1个回答

  • (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