Question

ВСЕ ЧТО ОСТАЛОСЬ класс алгебра

Answer 1

1.

1.

$120^o= 120^o \cdot \frac{\pi}{180^o}=\frac{12\pi }{18}=\frac{2\pi}{3}$

2.

$27^o=27^o\cdot \frac{\pi}{180}=\frac{3\pi}{20}$

3.

$210^o=210^o\cdot \frac{\pi}{180^o}=\frac{21\pi}{18}=\frac{7\pi}{6}$

4.

$300^o=300^o\cdot \frac{\pi}{180^o}=\frac{30 \pi}{18}=\frac{5\pi}{3}$

2.

$\frac{\cos{(\pi-\alpha)}\cdot tg (\pi+\alpha)}{\sin{(\frac{\pi}{2}-\alpha)}}=\frac{-\cos{\alpha}\cdot tg \alpha}{\cos{\alpha}}=-tg \alpha$

3.

a)

$\cos{40^o}\cdot\cos{20^o}-\sin{40^o}\cdot\sin{20^o}=\cos{(40^o+20^o)}=\cos{60^o}=\frac{1}{2}$

б)

$\sin{105^o}=\sin{(60^o+45^o)}=\sin{60^o}\cdot \cos{45^o}+\cos{60^o}\cdot\sin{45^o}=\frac{\sqrt{3}}{2}\cdot \frac{\sqrt{2}}{2}+\frac{1}{2}\cdot\frac{\sqrt{2}}{2}=\\ \\ =\frac{\sqrt{6}+\sqrt{2}}{4}$

4.

a)

$\frac{\sin{2\alpha}}{2tg\alpha}=\frac{2\cdot \sin{\alpha}\cdot \cos{\alpha}}{2\cdot \frac{\sin{\alpha}}{\cos{\alpha}}}=\frac{2\cdot \sin{\alpha}\cdot \cos{\alpha} \cdot \cos{\alpha}}{2\cdot \sin{\alpha}}=\cos^2{\alpha}$

б)

$\frac{1+\cos{2\alpha}}{1-\cos{2\alpha}}=\frac{1+(\cos^2{\alpha}-\sin^2{\alpha})}{1-(\cos^2{\alpha}-\sin^2{\alpha})}=\frac{1+\cos^2{\alpha}-\sin^2{\alpha}}{1-\cos^2{\alpha}+\sin^2{\alpha}}=\frac{1+\cos^2{\alpha}-(1-\cos^2{\alpha})}{\sin^2{\alpha}+\sin^2{\alpha}}=\frac{1+\cos^2{\alpha}-1+\cos^2{\alpha}}{2\sin^2{\alpha}}=\\ \\ =\frac{2\cos^2{\alpha}}{2\sin^2{\alpha}}=ctg^2\alpha$