Question

高中数学，求大神做一下这三道题，谢谢

高中数学，求大神做一下这三道题，谢谢高中数学，求大神做一下这三道题

Answer 1

(1)

sinα-3cosα=0

sinα=3cosα

tanα=sinα/cosα=3

1/(1-sinα)+ 1/(1+sinα)

=(1+sinα+1-sinα)/[(1-sinα)(1+sinα)]

=2/(1-sin²α)

=2(sin²α+cos²α)/cos²α

=2(tan²α +1)

=2·(3²+1)

=20

(2)

-π/2<α<0，sinα<0，cosα>0

sinα+cosα=1/5>0，-π/4<α<0

-1<tanα<0

(sinα+cosα)²/(sin²α+cos²α)=(1/5)²/1

(sin²α+cos²α+2sinαcosα)/(sin²α+cos²α)=1/25

(tan²α+1+2tanα)/(tan²α+1)=1/25

12tan²α+25tanα+12=0

(3tanα+4)(4tanα+3)=0

tanα=-4/3(舍去)或tanα=-¾

tanα=-¾

(3)

[(1-2sinαcosα)/(cos²α-sin²α)]·[(1+2sinαcosα)/(2sin²α-1)]

=[(1-2sinαcosα)(1+2sinαcosα)]/[(cos²α-sin²α)(2sin²α-1)]

=[(sinα-cosα)²(sinα+cosα)²]/[cos2α·(-cos2α)]

=[(sinα-cosα)(sinα+cosα)]²/(-cos²2α)

=(sin²α-cos²α)²/(-cos²2α)

=(-cos2α)²/(-cos²2α)

=cos²2α/(-cos²2α)

=-1