∵cos4θ=

1

5

=1-2sin²2θ，∴sin²2θ=

2

5

．

sin⁴θ+cos⁴θ=（sin²θ+cos²θ）²-2sin²θ•cos²θ=1-

1

2

sin²2θ=1-

1

5

=

4

5

，

故选A．