Question

已知cos(π+α)=-1/2 计算sin(2π+α)-tan(α-3π)的值

Answer 1

∵cos(π+α)=-cosα

∴-cosα=-1/2

cosα=1/2

∴α=π/3或α=-π/3

sin(2π+α)-tan(α-3π)

=sinα+tan(3π-α)

=sinα+tan(2π+π-α)

=sinα+tan(π-α)

=sinα-tanα

则当α=π/3时,

sin(2π+α)-tan(α-3π)

=sinπ/3-tanπ/3

=√3/2-√3

=-√3/2

则当α=-π/3时,

sin(2π+α)-tan(α-3π)

=sin(-π/3)-tan(-π/3)

=-sinπ/3+tanπ/3

=-√3/2+√3

=√3/2