Упр.434 ГДЗ Алимов 10-11 класс (Алгебра)

1) 3 sin пи/6 + 2cos пи/6 — tg пи/3;
2) 5sin пи/4 + 3tg пи/4 — 5cos пи/4 — 10ctg пи/4;
3) (2tg пи/6-tg пи/3):cos пи/6;
4) sin пи/3 * cos пи/6 — tg пи/4.

1. $$3\sin\frac{\pi}{6}+2\cos\frac{\pi}{6}-\tg\frac{\pi}{3} =3\cdot\frac12+2\cdot\frac{\sqrt3}{2}-\sqrt3 =\frac32+\sqrt3-\sqrt3=\frac32.$$

2. $$5\sin\frac{\pi}{4}+3\tg\frac{\pi}{4}-5\cos\frac{\pi}{4}-10\ctg\frac{\pi}{4} =5\cdot\frac{\sqrt2}{2}+3\cdot1-5\cdot\frac{\sqrt2}{2}-10\cdot1=-7.$$

3. $$ \left(2\tg\frac{\pi}{6}-\tg\frac{\pi}{3}\right):\cos\frac{\pi}{6} =\left(2\cdot\frac{1}{\sqrt3}-\sqrt3\right):\frac{\sqrt3}{2} $$
   $$ =\left(\frac{2}{\sqrt3}-\sqrt3\right)\cdot\frac{2}{\sqrt3} =\frac{4}{3}-2=-\frac{2}{3}. $$

4. $$\sin\frac{\pi}{3}\cdot\cos\frac{\pi}{6}-\tg\frac{\pi}{4} =\frac{\sqrt3}{2}\cdot\frac{\sqrt3}{2}-1 =\frac34-1=-\frac14.$$

Ответ

1) $$\frac32$$; 2) $$-7$$; 3) $$-\frac23$$; 4) $$-\frac14$$.