f(x)=cos^6 x+sin^6 x,求f(x)的最小正周期答案是π/2我算出来是π说哈怎么回事嘛,
问题描述：
f(x)=cos^6 x+sin^6 x,求f(x)的最小正周期
答案是π/2
我算出来是π
说哈怎么回事嘛,
答
f(x)=cos^6 x+sin^6 x
=(cos^2 x+sin^2 x)(cos^4 x-sin^2xcos^2x+sin^4 x)
=cos^4 x-sin^2xcos^2x+sin^4 x
=cos^4 x+2sin^2xcos^2x+sin^4 x-3sin^2xcos^2x
=(cos^2 x+sin^2 x)^2-3sin^2xcos^2x
=1-3sin^2xcos^2x
=1-3/4sin^2(2x)
=1-3/8(1-cos4x)
=5/8+3/8cos4x
f(x)的最小正周期是2π/4=π/2