若sin(3π-α)=根号2sin(2π+β)
问题描述：
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
答
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(sin...