若sin(3π-2)=根号2sin(2π+β),根号3cos(-α)=-根号2cos(π+β)0
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若sin(3π-2)=根号2sin(2π+β),根号3cos(-α)=-根号2cos(π+β)0
若sin(3π-2)=根号2sin(2π+β),根号3cos(-α)=-根号2cos(π+β)
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若sin(3π-2)=根号2sin(2π+β),根号3cos(-α)=-根号2cos(π+β)0
sin(3π-a)=根号2sin(2π+β),根号3cos(-α)=-根号2cos(π+β)
∴sina=√2sinβ ①
√3cosa=√2cosβ ②
①²+②²
sin²a+3cos²a=2=2sin²a+2cos²a
∴ sin²a=cos²a
∴ tana=1或-1
(1)tana=1
则a=π/4
∴ √2/2=√2sinβ,
∴ sinβ=1/2,
∴ sinasinβ=(√2/2)*(1/2)=√2/2
(2)tana=-1
则a=3π/4
∴ √2/2=√2sinβ,
∴ sinβ=1/2,
∴ sinasinβ=(√2/2)*(1/2)=√2/2
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