已知3tana=2tan(a+b),求证:sin(2a+b)=5sinb
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已知3tana=2tan(a+b),求证:sin(2a+b)=5sinb已知3tana=2tan(a+b),求证:sin(2a+b)=5sinb已知3tana=2tan(a+b),求证:sin(2a+
已知3tana=2tan(a+b),求证:sin(2a+b)=5sinb
已知3tana=2tan(a+b),求证:sin(2a+b)=5sinb
已知3tana=2tan(a+b),求证:sin(2a+b)=5sinb
证明:
已知3tana=2tan(a+b),
所以3sinacos(a+b)=2sin(a+b)cosa
得5sinacos(a+b)=2sin(a+b)cosa+2sinacos(a+b)=2sin(2a+b)
得sinacos(a+b)=2sin(a+b)cosa-2sinacos(a+b)=2sinb
两式相除有5=[2sin(2a+b)]/[2sinb]
即得sin(2a+b)=5sinb
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