已知sinα=3/5且π/2
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![已知sinα=3/5且π/2](/uploads/image/z/10148661-45-1.jpg?t=%E5%B7%B2%E7%9F%A5sin%CE%B1%3D3%2F5%E4%B8%94%CF%80%2F2)
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