Упр.608 ГДЗ Алимов 10-11 класс (Алгебра)

1. $$6\operatorname{arctg}\sqrt{3}-4\arcsin\left(-\frac{1}{\sqrt{2}}\right)$$
2. $$2\operatorname{arctg}1+3\arcsin\left(-\frac{1}{2}\right)$$
3. $$5\operatorname{arctg}(-\sqrt{3})-3\arccos\left(-\frac{\sqrt{2}}{2}\right)$$

1) $$6\arctg\sqrt{3}-4\arcsin\left(-\frac{1}{\sqrt{2}}\right)=6\cdot\frac{\pi}{3}-4\cdot\left(-\frac{\pi}{4}\right)=2\pi+\pi=3\pi.$$

2) $$2\arctg 1+3\arcsin\left(-\frac{1}{2}\right)=2\cdot\frac{\pi}{4}+3\cdot\left(-\frac{\pi}{6}\right)=\frac{\pi}{2}-\frac{\pi}{2}=0.$$

3) $$5\arctg(-\sqrt{3})-3\arccos\left(-\frac{\sqrt{2}}{2}\right)=5\cdot\left(-\frac{\pi}{3}\right)-3\cdot\frac{3\pi}{4}=-\frac{5\pi}{3}-\frac{9\pi}{4}=-\frac{47\pi}{12}.$$

Ответ

1) $$3\pi$$; 2) $$0$$; 3) $$-\frac{47\pi}{12}$$.