Question

α为锐角，且满足sinα=3cosα，求sinα·cosα的值

Answer 1

把sinα=3cosα两边平方得(sina)^2=1-(cosa)^2=9(cosa)^2
解出(cosa)^2=1/10
sinα·cosα=3(cosa)^2=3/10

Answer 2

因为 sinα=3cosα
两边平方 (sinα)^2=9(cosα)^2
得 （cosα）^2=1/10
sinαcosα=3(（cosα）^2)=3/10

Answer 3

sinα=3cosα
tanα=sinα/cosα=3

sinαcosα
=sinαcosα/(sin^2α+cos^2α)
=tanα/(tan^2α+1)
=3/(3^2+1)
=3/10

Answer 4

sinα=3cosα
tanα = 1/3
sinα = 1/√10
cosα = 3/√10
sinα .cosα = 3/10

Answer 5

因为sinα与cosα不可能同时为零，故由sinα=3cosα得tanα=3，则sec^2 α=1+tan^2 α=10
sinα·cosα=3cosα·cosα=3cos^ α=3/10