Question

已知cos(π +α)=3/50,则tan(2π-α)的值是

Answer 1

sinα=√5/5

α为锐角 则cosα>0

(cosα)^2+(sinα)^2=1

cosα=2√5/5

sinβ=√10/10

α为锐角 则cosβ>0

(cosβ)^2+(sinβ)^2=1

cosβ=3√10/10

sin(α+β)=sinαcosβ+cosαsinβ

=√5/5*3√10/10+2√5/5*√10/10

=(5√50)/50

=5/√50

=5/(5√2)

=√2/2

α、β都是区间(0,π/6)的角

0所以α+β= π/4

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