已知α属于(π/2,π),且sinα/2+cosα/2=2根号3/3(1)求cosα的值(2)若sin(α+β)=-3/5β属于(0,π/2),求sinβ的值.
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![已知α属于(π/2,π),且sinα/2+cosα/2=2根号3/3(1)求cosα的值(2)若sin(α+β)=-3/5β属于(0,π/2),求sinβ的值.](/uploads/image/z/6865471-55-1.jpg?t=%E5%B7%B2%E7%9F%A5%CE%B1%E5%B1%9E%E4%BA%8E%28%CF%80%2F2%2C%CF%80%29%2C%E4%B8%94sin%CE%B1%2F2%2Bcos%CE%B1%2F2%3D2%E6%A0%B9%E5%8F%B73%2F3%281%29%E6%B1%82cos%CE%B1%E7%9A%84%E5%80%BC%282%29%E8%8B%A5sin%28%CE%B1%2B%CE%B2%29%3D-3%2F5%CE%B2%E5%B1%9E%E4%BA%8E%280%2C%CF%80%2F2%29%2C%E6%B1%82sin%CE%B2%E7%9A%84%E5%80%BC.)
已知α属于(π/2,π),且sinα/2+cosα/2=2根号3/3(1)求cosα的值(2)若sin(α+β)=-3/5β属于(0,π/2),求sinβ的值.
已知α属于(π/2,π),且sinα/2+cosα/2=2根号3/3(1)求cosα的值(2)若sin(α+β)=-3/5
β属于(0,π/2),求sinβ的值.
已知α属于(π/2,π),且sinα/2+cosα/2=2根号3/3(1)求cosα的值(2)若sin(α+β)=-3/5β属于(0,π/2),求sinβ的值.
1.sinα/2+cosα/2=2根号3/3 平方
1+sina=4/3
sina=1/3 α属于(π/2,π),cosa
(sinα/2+cosα/2)^2=(2根号3/3)^2 sina=1/3 cosa= -2根号2/3
sin(α+β)=-3/5 sinαcosβ+cosαsinβ=-3/5 cosβ/3-2根号2sinβ/3=-3/5
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(sinα/2+cosα/2)^2=(2根号3/3)^2 sina=1/3 cosa= -2根号2/3
sin(α+β)=-3/5 sinαcosβ+cosαsinβ=-3/5 cosβ/3-2根号2sinβ/3=-3/5
2根号2cosβ/3-8sinβ/3=-6根号2/5
cos(α+β)=-4/5 cosαcosβ-sinαsinβ=-4/5 -2根号2cosβ/3-sinβ/3=-4/5
sinβ=(-6根号2-4)/15
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