3sin(a)^2+2sin(b)^2=1,3sin(a)=2sin(b),a,b都为锐角,求a+2b的值是3sin(2a)=2sin(2b),

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3sin(a)^2+2sin(b)^2=1,3sin(a)=2sin(b),a,b都为锐角,求a+2b的值是3sin(2a)=2sin(2b),
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3sin(a)^2+2sin(b)^2=1,3sin(a)=2sin(b),a,b都为锐角,求a+2b的值是3sin(2a)=2sin(2b),
3sin(a)^2+2sin(b)^2=1,3sin(a)=2sin(b),a,b都为锐角,求a+2b的值
是3sin(2a)=2sin(2b),

3sin(a)^2+2sin(b)^2=1,3sin(a)=2sin(b),a,b都为锐角,求a+2b的值是3sin(2a)=2sin(2b),
∵3sin²A+2sin²B=1
∴3sin²A=cos(2B) ①
∵3sin(2A)=2sin(2B)
∴3sinAcosA=sin(2B) ②
①/②,得
tanA=cot(2B)
∵A为锐角,
∴cot(2B)=tanA>0
∴2B也是锐角
∴A+2B=90°