已知tanα+1/tanα=5/2,α∈（π/4,π/2）,求cos2α及sin(2α+π/4)的值.

tanα+1/tanα=5/2sinα/cosα+cosα/sinα=5/2 通分得(sin²α+cos²α)/sinαcosα=5/21/sinαcosα=5/22sinαcosα=4/5sin2α=4/5因为α∈（π/4,π/2）,所以2α∈（π/2,π/）,cos2α=±√1-sin²α...