已知cos(5π/12-α)=m(lml≤1),求cos(π/12+α)和cos(11π/12-α)的值

题目

已知cos(5π/12-α)=m(lml≤1),求cos(π/12+α)和cos(11π/12-α)的值

答案

π/12+α+(5π/12-α)=π/2,
11π/12-α-(5π/12-α)=π/2,
∴cos(π/12+α)=sin(5π/12-α)=土√(1-m^2),
cos(11π-α)=-sin(5π/12-α)=干√(1-m^2).