tanα=1/2,则sin2α+cos²α的值是?

tanα=1/2,则sin2α+cos²α的值是?
tanα=1/2,则sin2α+cos²α的值是?

tanα=1/2,则sin2α+cos²α的值是?
sin2α+cos²α
＝(sin2α+cos²α)/1
=(2sinacosa+cos^2a)/(sin^2a+cos^2a)
=(2tana+1)/(tan^2a+1)
=8/5

sin2a=2tana/(1+tana^2)=1/(1+1/2^2)=4/5
cos2a=(1-tan^2 a)/(1+tan^2 a)=(1-1/4)/(1+1/4)=3/5
cos^2 a=(1+cos2a)/2=(1+3/5)/2=4/5
sin2a+cos^2 a=4/5+4/5=8/5

sin2α+cos²α=(2sinαcosα+cos²α)/(cos²α+sin²α)
=(2tanα+1)/(1+tan²α)
=2/(5/4)=8/5

sin2α+cos²α
＝(sin2α+cos²α)/1
=(2sinacosa+cos^2a)/(sin^2a+cos^2a)
=(2tana+1)/(tan^2a+1)
=8/5