将f(x)=(√3)/2*sin2x-1/2+(cosx)^2+1

问题描述:

将f(x)=(√3)/2*sin2x-1/2+(cosx)^2+1
将他化简,怎么化,基本公式我知道,请推导详细点,

f(x)=(√3)/2*sin2x-1/2+(cosx)^2+1
=√3/2sin2x-1/2+(cos2x+1)/2+1
=(√3/2)sin2x+(1/2)cos2x+1
=sin(2x+π/6)+1;
如果本题有什么不明白可以追问,√3/2)sin2x+(1/2)cos2x+1我化到这里了,你怎么推导出来的=sin(2x+π/6)+1=(√3/2)sin2x+(1/2)cos2x+1;√3/2=cosπ/6,1/2=sinπ/6;所以原式=cosπ/6sin2x+sinπ/6cos2x+1=sin(2x+π/6)+1;