Question

已知sin(α＋2/π)＝-√5/5,α∈(0,π),求cos∧2(π/4＋α/2)－cos∧2(π/4-α/2)/si

Answer 1

sin(α＋2/π)=cosα=-√5/5；

∴α∈(π/2,π)；

sinα=2√5/5；

cos^2(π/4＋α/2);

=1/2[cos(π/2+α)+1];

=1/2(1-sinα);

cos^2(π/4-α/2);

=1/2[cos(π/2-α)+1];

=1/2(1+sinα);

原式

=[1/2(1-sinα)-1/2(1+sinα)]/(sinα-cosα);

=-sinα/(sinα-cosα);

=-2√5/5/(2√5/5+√5/5);

=-2/3;