已知sinα=3/5且π/2

已知sinα=3/5且π/2
已知sinα=3/5且π/2<α<3/2π,求secα-tanα

已知sinα=3/5且π/2
sinα=3/5且π/2<α<3/2π,
所以
π/2<α<π,
而
sin²α+cos²α=1
即
cosα=-4/5
tanα=sinα/cosα=-3/4
secα=1/cosα=-5/4
所以
secα-tanα=-5/4+3/4=-1/2

π/2<α<3π/2
sinα=3/5
所以π/2<α<π
cosα=-4/5
tanα=-3/4
secα-tanα
=1/cosα-3/4
=1/(-4/5)-(-3/4)
=-5/4+3/4
=-1/2