若sin(3π-α)=根号2sin(2π+β)已知sin(3π-α)=根号2 sin(π-β),根号3 cos(-α)= - 根号2 cos(π+β) 且0

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若sin(3π-α)=根号2sin(2π+β)已知sin(3π-α)=根号2 sin(π-β),根号3 cos(-α)= - 根号2 cos(π+β) 且0

若sin(3π-α)=根号2sin(2π+β)已知sin(3π-α)=根号2 sin(π-β),根号3 cos(-α)= - 根号2 cos(π+β) 且0
若sin(3π-α)=根号2sin(2π+β)
已知sin(3π-α)=根号2 sin(π-β),根号3 cos(-α)= - 根号2 cos(π+β) 且0

若sin(3π-α)=根号2sin(2π+β)已知sin(3π-α)=根号2 sin(π-β),根号3 cos(-α)= - 根号2 cos(π+β) 且0
解:由sin(3π-α)=√2sin(2π+β)可得:
sinα=√2sinβ
由√3cos(-α)= -√2cos(π+β)可得:
√3cosα=√2cosβ
所以(sinα)^2+(cosα)^2=2/3+4(sinβ)^2/3=1
所以(sinβ)^2=1/4
所以sinα*sinβ=√2(sinβ)^2=√2/4