a,b为锐角,3sina+3sinb=1 ,3sin(2a)-2sin(2b)=0 求sin(a+2b)
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a,b为锐角,3sina+3sinb=1 ,3sin(2a)-2sin(2b)=0 求sin(a+2b)
![a,b为锐角,3sina+3sinb=1 ,3sin(2a)-2sin(2b)=0 求sin(a+2b)](/uploads/image/z/1847027-11-7.jpg?t=a%2Cb%E4%B8%BA%E9%94%90%E8%A7%92%2C3sina%2B3sinb%3D1+%2C3sin%282a%29-2sin%282b%29%3D0+%E6%B1%82sin%28a%2B2b%29)
明如下由COS(A+B)=0,有:
COS(A+B)=cosAcosB-sinAsinB=0
所以cosAcosB=sinAsinB
SIN(A+2B)=sinAcos2B+sin2BcosA
=sinA[(cosB)^2-(sinB)^2]+2sinBcosBcosA
=sinA[(cosB)^2-(sinB)^2]+2sinA(sinB)^2
=sinA[(cosB)^2-(sinB)^2+2(sinB)^2]
=sinA[(cosB)^2+(sinB)^2]
=sinA
COS(A+B)=cosAcosB-sinAsinB=0
所以cosAcosB=sinAsinB
SIN(A+2B)=sinAcos2B+sin2BcosA
=sinA[(cosB)^2-(sinB)^2]+2sinBcosBcosA
=sinA[(cosB)^2-(sinB)^2]+2sinA(sinB)^2
=sinA[(cosB)^2-(sinB)^2+2(sinB)^2]
=sinA[(cosB)^2+(sinB)^2]
=sinA
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