488. Найти значение выражения: 1) sin(π/4) cos(π/4) − sin(π/3) cos(π/6); 2) 2 tg²(π/3) − ctg²(π/6) − sin(π/6) cos(π/3); 3) (tg(π/4) − ctg(π/3))(ctg(π/4) + tg(π/6)); 4) 2 cos²(π/6) − sin²(π/3) + tg(π/6) ctg(π/3).

Question

Вопрос:

Accepted Answer

\(\frac{\sqrt2}{2}\cdot\frac{\sqrt2}{2}-\frac{\sqrt3}{2}\cdot\frac{\sqrt3}{2}=\frac14-\frac34=-\frac12\).
\(2\cdot3-3-\frac12\cdot\frac12=6-3-\frac14=\frac{11}{4}\).
\(\left(1-\frac1{\sqrt3}\right)\left(1+\frac1{\sqrt3}\right)=1-\frac13=\frac23\).
\(2\cdot\frac34-\frac34+\frac1{\sqrt3}\cdot\frac1{\sqrt3}=\frac32-\frac34+\frac13=\frac{13}{12}\).

Ответ: 1) \(-\frac12\); 2) \(\frac{11}{4}\); 3) \(\frac23\); 4) \(\frac{13}{12}\).