求证8cos的4次方a=coa4a+4cos2a+3
问题描述：
求证8cos的4次方a=coa4a+4cos2a+3
答
cos(4a)+4cos(2a)+3
=2cos^2(2a)-1+4(2cos^2a-1)+3
=2[(2cos^2a-1)^2]-1+8cos^2a-4+3
=2[4cos^4a-4cos^2a+1]-1+8cos^2a-4+3
=8cos^4a-3+3
=8cos^4a