1) sin(α+β)+sin(α-β)=
=sin(α)cos(β)+sin(β)cos(α)+sin(α)cos(β)-sin(β)cos(α)=
=2sin(α)cos(β)
2) [sin(3π/2+α)+sin(2π+α)]/[2sin(-α)cos(-α)+1]=
=[-cos(α)+sin(α)]/[-2sin(α)cos(α)+sin²(α)+cos²(α)]=
=[-cos(α)+sin(α)]/[sin(α)-cos(α)]²=1/[sin(α)-cos(α)]=
=1/[√2sin(α-π/4)]
или -1/[√2cos(α+π/4)]
3) sin(2α)/[1+cos(2α)]= sin(2α)/[2cos²(α)]=
=2sin(α)cos(α)/[2cos²(α)]=1/cos(α)