Question

函数y=2sin(x+π/4)cos(π/4-x)图像的一条对称轴

Answer 1

【解】

y=2sin(x+π/4)cos(π/4-x)

=2sin(x+π/4)cos(π/2-( x+π/4))

=2sin(x+π/4)sin(x+π/4)

=2sin²(x+π/4)

=1-cos[2(x+π/4)]

=1-cos[2x+π/2]

=1+sin(2x),

令2x=kπ+π/2,k∈Z.

x=kπ/2+π/4,k∈Z.

函数y=2sin(x+π/4)cos(π/4-x)图像的对称轴是x=kπ/2+π/4,k∈Z.