已知a.b为锐角,tan a =1/7,sin b =√10/10,求tan (a +2b )的值,

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已知a.b为锐角,tan a =1/7,sin b =√10/10,求tan (a +2b )的值,
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已知a.b为锐角,tan a =1/7,sin b =√10/10,求tan (a +2b )的值,
已知a.b为锐角,tan a =1/7,sin b =√10/10,求tan (a +2b )的值,

已知a.b为锐角,tan a =1/7,sin b =√10/10,求tan (a +2b )的值,
tan a =1/7 sin b =√10/10
所以cosb=3√10/10
所以sin2b=2sinbcosb=3/5
cos2b=1-2sin^2b=4/5
tan2b=sin2b/cos2b=3/4
tan(a+2b)=(tana+tan2b)/(1-tanatan2b)=(1/7+3/4)/(1-1/7×3/4)=1