Упр.1288 ГДЗ Макарычев Миндюк 9 класс (Углубленный) (Алгебра)

а) 1/2sin(?/4)cos(?/4); г) 8cos(?/2)ctg(?/4); ж) sin(?/3)cos(?/3)tg(?/3);
б) 1/3tg(?/3)ctg(?/6); д) sin(?/3)(tg(?/6)-cos(?/6)); з) cos(?/6)-tg(?/6)+ctg(?/6)?
в) 4tg(?/6)sin(?/3); е) tg(?/6)(cos(?/4)+sin(?/4));

1. а)

   $$\frac12\sin\frac{\pi}{4}\cos\frac{\pi}{4} =\frac12\cdot\frac{\sqrt2}{2}\cdot\frac{\sqrt2}{2} =\frac18.$$

2. б)

   $$\frac13\tg\frac{\pi}{3}\ctg\frac{\pi}{6} =\frac13\cdot\sqrt3\cdot\sqrt3 =1.$$

3. в)

   $$4\tg\frac{\pi}{6}\sin\frac{\pi}{3} =4\cdot\frac{\sqrt3}{3}\cdot\frac{\sqrt3}{2} =2.$$

4. г)

   $$8\cos\frac{\pi}{2}\ctg\frac{\pi}{4} =8\cdot0\cdot1 =0.$$

5. д)

   $$\sin\frac{\pi}{3}\left(\tg\frac{\pi}{6}-\cos\frac{\pi}{6}\right) =\frac{\sqrt3}{2}\left(\frac{\sqrt3}{3}-\frac{\sqrt3}{2}\right) =\frac{3}{6}-\frac{3}{4} =-\frac14.$$

6. е)

   $$\tg\frac{\pi}{6}\left(\cos\frac{\pi}{4}+\sin\frac{\pi}{4}\right) =\frac{\sqrt3}{3}\left(\frac{\sqrt2}{2}+\frac{\sqrt2}{2}\right) =\frac{\sqrt6}{6}+\frac{\sqrt6}{6} =\frac{\sqrt6}{3}.$$

7. ж)

   $$\sin\frac{\pi}{3}\cos\frac{\pi}{3}\tg\frac{\pi}{3} =\frac{\sqrt3}{2}\cdot\frac12\cdot\sqrt3 =\frac34.$$

8. з)

   $$\cos\frac{\pi}{6}-\tg\frac{\pi}{6}+\ctg\frac{\pi}{6} =\frac{\sqrt3}{2}-\frac{\sqrt3}{3}+\sqrt3 =\frac{7\sqrt3}{6}.$$

Ответ

а) $$\frac18$$; б) $$1$$; в) $$2$$; г) $$0$$; д) $$-\frac14$$; е) $$\frac{\sqrt6}{3}$$; ж) $$\frac34$$; з) $$\frac{7\sqrt3}{6}$$.