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的四次方α=

已知tanα=根号3，α为第三象限，则sinα=
已知sinα+cosα=二分之根号二,求sin的平方α分之1+cos的平方α分之1= （求过程）

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