求证 2(sinx)^4+3/4sin(2x)^2+5cosx^4-1/2cos4x-1/2cos2x=2(1+cosx^2)
求证 2(sinx)^4+3/4sin(2x)^2+5cosx^4-1/2cos4x-1/2cos2x=2(1+cosx^2)
日期：2021-04-24 11:49:39 人气：1
3/4sin(2x)^2=3/4(2sinxcosx)^2=3(sinxcosx)^2
所以左边=2(sinx)^4+4(sinxcosx)^2+2(cosx)^4-(sinxcosx)^2+3(cosx)^4-1/2[2(cos2x)^2-1]-1/2cos2x
=2[(sinx)^2+(cosx)^2]^2-(sinxcosx)^2+3(cosx)^4-(cos2x)^2+1/2-1/2[2(cosx)^2-1]
=2*1
所以左边=2(sinx)^4+4(sinxcosx)^2+2(cosx)^4-(sinxcosx)^2+3(cosx)^4-1/2[2(cos2x)^2-1]-1/2cos2x
=2[(sinx)^2+(cosx)^2]^2-(sinxcosx)^2+3(cosx)^4-(cos2x)^2+1/2-1/2[2(cosx)^2-1]
=2*1