1. Тип 7 № 26755 Найдите значение выражения (12sin 11° - cos 11°) / sin 22°.

1. $\frac{12\sin 11^\circ \cdot \cos 11^\circ}{\sin 22^\circ} = \frac{6\sin 22^\circ}{\sin 22^\circ} = 6$. Ответ: 6. 2. $\frac{24(\sin^2 17^\circ - \cos^2 17^\circ)}{\cos 34^\circ} = \frac{-24(\cos^2 17^\circ - \sin^2 17^\circ)}{\cos 34^\circ} = \frac{-24\cos 34^\circ}{\cos 34^\circ} = -24$. Ответ: -24. 3. $\frac{5\cos 29^\circ}{\sin 61^\circ} = \frac{5\cos 29^\circ}{\sin(90^\circ - 29^\circ)} = \frac{5\cos 29^\circ}{\cos 29^\circ} = 5$. Ответ: 5. 4. $36\sqrt{6} \cdot \text{tg} \frac{\pi}{6} \cdot \sin \frac{\pi}{4} = 36\sqrt{6} \cdot \frac{\sqrt{3}}{3} \cdot \frac{\sqrt{2}}{2} = 36 \cdot \frac{\sqrt{18}}{6} = 6 \cdot 3\sqrt{2} = 18\sqrt{2}$. Ответ: 18\sqrt{2}. 5. $4\sqrt{2} \cos \frac{\pi}{4} \cos \frac{7\pi}{3} = 4\sqrt{2} \cdot \frac{\sqrt{2}}{2} \cdot \cos(2\pi + \frac{\pi}{3}) = 4 \cdot \cos \frac{\pi}{3} = 4 \cdot \frac{1}{2} = 2$. Ответ: 2. 6. $\frac{8}{\sin(-\frac{27\pi}{4}) \cos(\frac{31\pi}{4})} = \frac{8}{(-\sin(6\pi + \frac{3\pi}{4})) \cos(8\pi - \frac{\pi}{4})} = \frac{8}{(-\sin \frac{3\pi}{4}) \cos(-\frac{\pi}{4})} = \frac{8}{(-\frac{\sqrt{2}}{2}) \cdot \frac{\sqrt{2}}{2}} = \frac{8}{-1/2} = -16$. Ответ: -16. 7. $-4\sqrt{3} \cos(-750^\circ) = -4\sqrt{3} \cos(750^\circ) = -4\sqrt{3} \cos(2 \cdot 360^\circ + 30^\circ) = -4\sqrt{3} \cos 30^\circ = -4\sqrt{3} \cdot \frac{\sqrt{3}}{2} = -2 \cdot 3 = -6$. Ответ: -6. 8. $2\sqrt{3} \text{tg}(-300^\circ) = -2\sqrt{3} \text{tg}(300^\circ) = -2\sqrt{3} \text{tg}(360^\circ - 60^\circ) = -2\sqrt{3} \cdot (-\text{tg} 60^\circ) = 2\sqrt{3} \cdot \sqrt{3} = 6$. Ответ: 6. 9. $-18\sqrt{2} \sin(-135^\circ) = 18\sqrt{2} \sin 135^\circ = 18\sqrt{2} \sin(180^\circ - 45^\circ) = 18\sqrt{2} \sin 45^\circ = 18\sqrt{2} \cdot \frac{\sqrt{2}}{2} = 9 \cdot 2 = 18$. Ответ: 18. 10. $24\sqrt{2} \cos(-\frac{\pi}{3}) \sin(-\frac{\pi}{4}) = 24\sqrt{2} \cos \frac{\pi}{3} \cdot (-\sin \frac{\pi}{4}) = 24\sqrt{2} \cdot \frac{1}{2} \cdot (-\frac{\sqrt{2}}{2}) = -6 \cdot 2 = -12$. Ответ: -12. 11. $\frac{14\sin 19^\circ}{\sin 341^\circ} = \frac{14\sin 19^\circ}{\sin(360^\circ - 19^\circ)} = \frac{14\sin 19^\circ}{-\sin 19^\circ} = -14$. Ответ: -14. 12. $\frac{4\cos 146^\circ}{\cos 34^\circ} = \frac{4\cos(180^\circ - 34^\circ)}{\cos 34^\circ} = \frac{4(-\cos 34^\circ)}{\cos 34^\circ} = -4$. Ответ: -4. 13. $\frac{5\text{tg} 163^\circ}{\text{tg} 17^\circ} = \frac{5\text{tg}(180^\circ - 17^\circ)}{\text{tg} 17^\circ} = \frac{-5\text{tg} 17^\circ}{\text{tg} 17^\circ} = -5$. Ответ: -5. 14. $\frac{14\sin 409^\circ}{\sin 49^\circ} = \frac{14\sin(360^\circ + 49^\circ)}{\sin 49^\circ} = \frac{14\sin 49^\circ}{\sin 49^\circ} = 14$. Ответ: 14. 15. $5\text{tg} 17^\circ \cdot \text{tg} 107^\circ = 5\text{tg} 17^\circ \cdot \text{tg}(90^\circ + 17^\circ) = 5\text{tg} 17^\circ \cdot (-\text{ctg} 17^\circ) = 5\text{tg} 17^\circ \cdot (-\frac{1}{\text{tg} 17^\circ}) = -5$. Ответ: -5. 16. $7\text{tg} 13^\circ \cdot \text{tg} 77^\circ = 7\text{tg} 13^\circ \cdot \text{tg}(90^\circ - 13^\circ) = 7\text{tg} 13^\circ \cdot \text{ctg} 13^\circ = 7 \cdot 1 = 7$. Ответ: 7. 17. $\frac{12}{\sin^2 37^\circ + \sin^2 127^\circ} = \frac{12}{\sin^2 37^\circ + \sin^2(90^\circ + 37^\circ)} = \frac{12}{\sin^2 37^\circ + \cos^2 37^\circ} = \frac{12}{1} = 12$. Ответ: 12.