求证明cosxcos2xcos4.cos2^(n-1) x= sin 2^n x / 2^n sinx_数学解答

求证明cosxcos2xcos4.cos2^(n-1) x= sin 2^n x / 2^n sinx

人气：285 ℃　时间：2020-04-20 07:37:39

解答

cosxcos2xcos4.cos2^(n-1) x
=2sinxcosxcos2xcos4.cos2^(n-1) x/(2sinx)
=sin2xcos2xcos4.cos2^(n-1) x/(2sinx)
=sin4xcos4x.cos2^(n-1) x/(2^2sinx)
=sin2^(n-1) xcos2^(n-1) x/[2^(n-1)sinx]
=sin2^nx/(2^nsinx)