已知sinα=2sinβ,tanα=3tanβ,求αcos^2的值

sinα=2sinβ
sin^2β=sin^2α/4=(1-cos^2α）/4
cos^2β=1-sin^2β=1-(1-cos^2α）/4=(3+cos^2α）/4
tanα=3tanβ
(sinα/cosα)^2=(3sinβ/cosβ)^2
sin^2α/cos^2α=9sin^2β/cos^2β=(9sin^2α）/4)/[(3+cos^2α）/4]
cos^2α=3/8
（cosα）^2=3/8