已知a、β是锐角,a+β≠π/2,且满足tanβ=(sin2a)/(3-cos2a).证明：tan(a+β)=2tana

已知a、β是锐角,a+β≠π/2,且满足tanβ=(sin2a)/(3-cos2a).证明：tan(a+β)=2tana
已知a、β是锐角,a+β≠π/2,且满足tanβ=(sin2a)/(3-cos2a).证明：tan(a+β)=2tana

已知a、β是锐角,a+β≠π/2,且满足tanβ=(sin2a)/(3-cos2a).证明：tan(a+β)=2tana
tan(a+β)=(tana+tanβ)/(1-tana *tanβ),将tanβ=(sin2a)/(3-cos2a)带入原式得,[tana+sin2a/(3-cos2a)]/{1-tana*[(sin2a)/(3-cos2a)]},分母下边的化简得1-(sina/cosa)*(2sina*cosa/3-cos2a)=2/(3-cos2a)
分母上边的化简得(3tana-tana*cos2a+sin2a)/(3-cos2a)=4tana/(3-cos2a)
所以得tan(a+β)=[4tana/(3-cos2a)]/2/(3-cos2a)=2tana