Question

Преобразовать в произведение: cos(a)+sin(a)-cos2(pi)

Answer 1

cos(α)+sin(α)-cos(2π);

1)cos(α)-cos(2π)=-2sin((α+2π)/2)sin((α-2π)/2)=-2sin(α/2+π)sin(α/2-π)=

=2sin(π+α/2)sin(π-α/2)=-2sin(α/2)sin(α/2);

2)sin(α)=2sin(α/2)cos(α/2);

1+2) 2sin(α/2)cos(α/2)-2sin(α/2)sin(α/2)=2sin(α/2)(cos(α/2)-sin(α/2));