sinα+cosα-sin(α-π/6)+cos(α-π/6)=√6cos(α-π/12);

sinα-sin(α-π/6)+cosα+cos(α-π/6)=

2sin((a-a+π/6)/2)cos((a+a-π/6)/2)+2cos((a+a-π/6)/2)cos((a-a+π/6)/2)=

2sin(π/12)cos(a-π/12)+2cos(a-π/12)cos(π/12)=

2*(1/2)cos(a-π/12)+2(√3/2)cos(a-π/12)=

cos(a-π/12)+√3cos(a-π/12)=(1+√3)cos(a-π/12);

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(1+√3)cos(a-π/12)≠√6cos(α-π/12);

1+√3≠√6;

Может неправильно переписали?