Упр.533 ГДЗ Алимов 10-11 класс (Алгебра)

2) sin(5пи/4 + a)= -sin(3пи/4 — a);
3) cos(a- 2пи/3)= -cos(пи/3 + a);
4) cos(a- 2пи/3)= cos(a+ 4пи/3).

1. $$\sin\left(\frac{7\pi}{6}+a\right)=\sin\left(\pi+\left(\frac{\pi}{6}+a\right)\right)=-\sin\left(\frac{\pi}{6}+a\right).$$

2. $$\sin\left(\frac{5\pi}{4}+a\right)=\sin\left(2\pi+\left(-\frac{3\pi}{4}+a\right)\right)=-\sin\left(\frac{3\pi}{4}-a\right).$$

3. $$\cos\left(a-\frac{2\pi}{3}\right)=\cos\left(-2\pi+\left(\frac{4\pi}{3}+a\right)\right)=-\cos\left(\frac{\pi}{3}+a\right).$$

4. $$\cos\left(a-\frac{2\pi}{3}\right)=\cos\left(-2\pi+\left(\frac{4\pi}{3}+a\right)\right)=\cos\left(a+\frac{4\pi}{3}\right).$$

Ответ

1) $$\sin\left(\frac{7\pi}{6}+a\right)=-\sin\left(\frac{\pi}{6}+a\right);$$
2) $$\sin\left(\frac{5\pi}{4}+a\right)=-\sin\left(\frac{3\pi}{4}-a\right);$$
3) $$\cos\left(a-\frac{2\pi}{3}\right)=-\cos\left(\frac{\pi}{3}+a\right);$$
4) $$\cos\left(a-\frac{2\pi}{3}\right)=\cos\left(a+\frac{4\pi}{3}\right).$$