Question

已知sinαcosα=1/8,则cosα+sinα的值等于 若sinα+sin的平方α=1,则cos的平方α+cos的四

Answer 1

sinαcosα=1/8

2sinαcosα=1/4

1+2sinαcosα=1/4

(sinα)^2+(cosα)^2+2sinαcosα=1/4

(sinα+cosα)^2=1/4

sinα+cosα=±1/2

sinα+(sinα)^2=1

sinα=1-(sinα)^2

sinα=(cosα)^2平方

sinα=(cosα)^2

(sinα)^2=(cosα)^4

(cosα)^4-(sinα)^2=0

(cosα)^4+1-(sinα)^2=1

(cosα)^4+(cosα)^2=1

tanα=根号3,α为第三象限,则sinα=-根号3/2

sinα+cosα=二分之根号二（平方）

(sinα)^2+(cosα)^2+2sinαcosα=1/2

1+2sinαcosα=1/2

2sinαcosα=-1/2

sinαcosα=-1/4

1/(sinα)^2+1/(cosα)^2

=(cosα)^2/[(cosα)^2(sinα)^2]+(sinα)^2/[(cosα)^2(sinα)^2]

=[(cosα)^2+(sinα)^2]/[(cosα)^2(sinα)^2]

=1/(cosαsinα)^2

=1/(-1/4)^2

=1/(1/16)

=16