分类：教育/科学-理工学科-数学
问题：求三角函数的值域请问：已知函数y=2cos平方x+6sinxco 
请问：已知y=2cos平方x+6sinxcosx+4cos(x+Π/4)cos(x-Π/4),求它的值域。
回答：y=2(cosx)^2+6sinxcosx+4cos(x+π/4)cos(x-π/4)
=cos2x+1+3sin2x+4cos(x-π/4+π/2)cos(x-π/4)
=cos2x+1+3sin2x-4sin(x-π/4)cos(x-π/4)
=1+cos2x+3sin2x-2sin(2x-π/2)
=1+cos2x+3sin2x+2cos2x
=3sin2x+3cos2x+1
=3√2sin(2x+π/4)+1,
值域为[-3√2+1,3√2+1]