sinα=2sinβ,tanα=3tanβ求(cosα)^2

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sinα=2sinβ,tanα=3tanβ求(cosα)^2

sinα=2sinβ,tanα=3tanβ求(cosα)^2
sinα=2sinβ,tanα=3tanβ
求(cosα)^2

sinα=2sinβ,tanα=3tanβ求(cosα)^2
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

解:tanα=3tanβ sinα/cosα=3sinβ/cosβ 因为sinα=2sinβ 所以2sinβ/cosα=3sinβ/cosβ 3/2cosα=cosβ sinβ^2+cosβ^=1 即1/4sinα^2+9/4cosα^2=1
又因为sinα^2+cosα^2=1 两式可得 (cosα)^2=3/8