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tan(a+b)=3,tan(a-b)=1/2,求sin2a/sin2b
人气:260 ℃ 时间:2020-10-01 18:58:51
解答
tan(a+b)=3,tan(a-b)=1/2,
tan2a=tan(a+b+a-b)=[tan(a+b)+tan(a-b)]/[1-tan(a+b)tan(a-b)]=(7/2)/(1-3/2)=-7
sin2a=-7/5√2,或7/5√2
同理
tan2b=tan(a+b-a+b)=[tan(a+b)-tan(a-b)]/[1+tan(a+b)tan(a-b)]=(5/2)/(1+3/2)=1
sin2b=√2/2,-√2/2
sin2a/sin2b=7/5或-7/5
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