a)
[tex]2\sin120^\circ*\cos30^\circ+3\sin135^\circ*\cos45^\circ=\\=2\sin(90^\circ+30^\circ)*\cos30^\circ+3\sin(90^\circ+45^\circ)*\cos45^\circ=\\=2\cos30^\circ*\cos30^\circ+3\cos45^\circ*\cos45^\circ=2\cos^230^\circ+3\cos^245^\circ=\\=2*(\frac{\sqrt3}{2})^2+3*(\frac{\sqrt2}{2})^2=2*\frac{3}{4}+3*\frac{2}{4}=\frac{6}{4}+\frac{6}{4}=\frac{12}{4}=3[/tex]
b)
[tex]\text{tg }150^\circ*\text{tg }60^\circ-\text{tg }45^\circ=\text{tg }(90^\circ+60^\circ)*\text{tg }60^\circ-1=-\text{ctg }60^\circ*\text{tg }60^\circ-1=\\=-1-1=-2[/tex]
