Упростить : (cos15°-cos75°)-(sin75°+sin15°)

[latex]15=45-30; \; 75 = 45+30;\\ (cos15-cos75)-(sin75+sin15)\\cos(45-30)-cos(45+30)-sin(45+30)+sin(45-30)=\\cos45cos30+sin45sin30-cos45cos30+sin45sin30-\\-sin45cos30-cos45sin30+sin45cos30-cos45sin30=\\=2sin45sin30+2sin45cos30=2*\frac{\sqrt2}{2}*\frac{1}{2}+2*\frac{\sqrt2}{2}*\frac{\sqrt3}{2}=\frac{\sqrt2+\sqrt6}{2}[/latex]