已知cosα=1/7,cos(α-β)=13/14,且0< β <α<π/2cos(π+2α)tan(π-2α)sin(π/2-2α)(1)求 ---------------------------------------- 的值cos(π/2+2α)(2)求角β
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已知cosα=1/7,cos(α-β)=13/14,且0< β <α<π/2cos(π+2α)tan(π-2α)sin(π/2-2α)(1)求 ---------------------------------------- 的值cos(π/2+2α)(2)求角β
已知cosα=1/7,cos(α-β)=13/14,且0< β <α<π/2
cos(π+2α)tan(π-2α)sin(π/2-2α)
(1)求 ---------------------------------------- 的值
cos(π/2+2α)
(2)求角β
已知cosα=1/7,cos(α-β)=13/14,且0< β <α<π/2cos(π+2α)tan(π-2α)sin(π/2-2α)(1)求 ---------------------------------------- 的值cos(π/2+2α)(2)求角β
(1)cos(π+2α)tan(π-2α)sin(π/2-2α)/cos(π/2+2α)
=[-cos(2α)][-tan(2α)]cos(2α)/[-sin(2α)] (应用诱导公式)
=-cos²(2α)[sin(2α)/cos(2α)]/sin(2α)
=-cos(2α)
=1-2cos²α (应用倍角公式)
=1-2*(1/7) (∵cosα=1/7)
=5/7;
(2)∵cosα=1/7,cos(α-β)=13/14,且0< β <α<π/2
∴sinα=√(1-cos²α)=4√3/7,sin(α-β)=√(1-cos²(α-β))=3√3/14
∵sinβ=sin(α-(α-β))
=sinαcos(α-β)-cosαsin(α-β)
=(4√3/7)(13/14)-(1/7)(3√3/14)
=√3/2
∴β=π/3.
已知cosα=7分之1,cos﹙α-β﹚=14分之13,且0<β<α<2分之π,则β等于多少
∵cos(α-β)= ,0<β<α< ,∴sin(α-β)= ,sinα= .
cosβ=cos[α-(α-β)]=cosαcos(α-β)+sinαsin(α-β)= ,
∴β=