若tanα+1/tanα=10/3,α属于45°到90°(开区间),则sin(2α+π/4)=
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![若tanα+1/tanα=10/3,α属于45°到90°(开区间),则sin(2α+π/4)=](/uploads/image/z/3709656-0-6.jpg?t=%E8%8B%A5tan%CE%B1%2B1%2Ftan%CE%B1%3D10%2F3%2C%CE%B1%E5%B1%9E%E4%BA%8E45%C2%B0%E5%88%B090%C2%B0%EF%BC%88%E5%BC%80%E5%8C%BA%E9%97%B4%EF%BC%89%2C%E5%88%99sin%282%CE%B1%2B%CF%80%2F4%29%3D)
若tanα+1/tanα=10/3,α属于45°到90°(开区间),则sin(2α+π/4)=
若tanα+1/tanα=10/3,α属于45°到90°(开区间),则sin(2α+π/4)=
若tanα+1/tanα=10/3,α属于45°到90°(开区间),则sin(2α+π/4)=
若tanα+1/tanα=10/3,α属于45°到90°(开区间),
tanα=3 sinα=3/(根10),cosα=1/(根10),
sin2α=3/5 cos2α=-4/5
sin(2α+π/4)=sin2α cosπ/4+cos2α sinπ/4=-根2/10
tanα+1/tanα=10/3 ∵α∈(45°,90°)
∴sinα/cosα+cosα/sinα=10/3 ∴2α∈(90°,180°)
∴(sin²α+cos²α)/sinα·cosα=10/3 ...
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tanα+1/tanα=10/3 ∵α∈(45°,90°)
∴sinα/cosα+cosα/sinα=10/3 ∴2α∈(90°,180°)
∴(sin²α+cos²α)/sinα·cosα=10/3 ∴cos2α=-4/5
∴1/sinα·cosα=10/3 ∴sin(2α+π/4)=sin2α·cosπ/4+cos2α·sinπ/4
∴sinα·cosα=3/10 =-(√2)/10
∴1/2sin2α=3/10
∴sin2α=3/5 (接右边)
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