№ 2.24 Геометрія = № 2.24 Математика
Обчисліть:
1) $\cos^{2}150^{\circ}-\sin^{2}120^{\circ}+\text{tg}135^{\circ}$;
2) $\text{tg}120^{\circ}\cdot\cos 120^{\circ}+\sin 120^{\circ}$.
Розв’язок:
1) $\cos^{2}150^{\circ}-\sin^{2}120^{\circ}+\text{tg}135^{\circ}=$
$=(-cos30^{\circ})^{2}-(sin60^{\circ})^{2}-\text{tg}45^{\circ}=$
$=\left(-\frac{\sqrt{3}}{2} \right)^{2}-\left( \frac{\sqrt{3}}{2} \right)^{2}-1=$
$=\frac{3}{4}-\frac{3}{4}-1=-1$
2) $\text{tg}120^{\circ}\cdot cos120^{\circ}+sin120^{\circ}=$
$=\frac{\sin 120^{\circ}}{\cos 120^{\circ}}\cdot cos120^{\circ}+sin120^{\circ}=$
$=sin120^{\circ}+sin120^{\circ}=2\sin 120^{\circ}=$
$=2sin(180^{\circ}-60^{\circ})=$
$=2\cdot sin60^{\circ}=2\cdot\frac{\sqrt{3}}{2}=\sqrt{3}$