若x,y满足log[4cos²(xy)+1/4cos²(xy)]=lny-y/2+ln(e²/2),则ycos4x的值为

题目

若x,y满足log[4cos²(xy)+1/4cos²(xy)]=lny-y/2+ln(e²/2),则ycos4x的值为

答案

好象等式右边的底数是2 log2 [4cos²(xy)+1/4cos²(xy)]=lny-y/2+ln(e²/2)令y=2 右=1 ∴4cos²(2x)+1/4cos²(2x)=2解得4cos²(2x)=1 cos4x=-1/2∴ycos4x=-1