Rút gọn biểu thức \(A = \frac{{1 - \cos \alpha + \cos 2\alpha }}{{\sin 2\alpha - \sin \alpha }}\)?
Hãy suy nghĩ và trả lời câu hỏi trước khi xem đáp án
\(\begin{array}{l}A = \frac{{1 - \cos \alpha + \cos 2\alpha }}{{\sin 2\alpha - \sin \alpha }} = \frac{{1 - \cos \alpha + 2{{\cos }^2}\alpha - 1}}{{2\sin \alpha \cos \alpha - \sin \alpha }}\\ = \frac{{2{{\cos }^2}\alpha - \cos \alpha }}{{2\sin \alpha \cos \alpha - \sin \alpha }} = \frac{{\cos \alpha \left( {2\cos \alpha - 1} \right)}}{{\sin \alpha \left( {2\cos \alpha - 1} \right)}} = \frac{{\cos \alpha }}{{\sin \alpha }} = \cot \alpha \end{array}\)
Chọn D.
Bộ Đề Kiểm Tra Giữa Học Kì I - Toán 10 - (Năm 2023 - 2024) - Các Trường THPT Trên Toàn Quốc là tài liệu giúp học sinh hệ thống lại các kiến thức đã học thông qua các câu hỏi ngắn gọn và súc tích. Các bài tập được thiết kế phù hợp với nhiều đối tượng học sinh, từ cơ bản đến nâng cao.
Câu hỏi liên quan
Một chiếc xe có khối lượng 100 kg đang chạy với vận tốc 54 km/h thì hãm phanh. Biết lực hãm có độ lớn là 450 N. Quãng đường từ khi hãm phanh đến lúc dừng lại hẳn là:
Quá trình chuyển hóa năng lượng trong động cơ đốt trong là?
Cho tứ diện ABCD. Gọi I, J là trung điểm của AC và AD. Xét các mệnh đề sau:(I) IJ // (BCD).(II) CD // (BCD)(III) Giao tuyến của (BCD) và (BIJ) là đường thẳng qua B song song với CD.
Read the following passage about the Exploring The Universe and mark the letter A, B, C or D on your answer sheet to indicate the best answer to each of the following questions from 31 to 40.
Science is a vast and fascinating field that seeks to understand the natural world and the universe beyond[I]. It encompasses various disciplines, including physics, chemistry, biology, and astronomy[II]. Each of these areas contributes to our understanding of complex phenomena, [III]. For instance, scientific research has led to significant breakthroughs in medicine, renewable energy, and environmental conservation[IV]. In this essay, we will explore the impact of science on our lives, particularly focusing on space exploration.
One of the most intriguing aspects of science is space exploration. Humans have always looked to the stars, wondering what lies beyond our planet. The launch of satellites and manned missions has allowed us to gather valuable information about the cosmos. For example, NASA's Mars Rover has provided insight into the potential for life on other planets. Through meticulous research and data collection, scientists can analyze soil samples and atmospheric conditions, paving the way for future explorations.
Space exploration also raises critical questions about our existence and the future of humanity. As we continue to advance technologically, the prospect of colonizing other planets becomes more plausible. This endeavor could serve as a solution to the challenges we face on Earth, such as overpopulation and resource depletion. However, ethical considerations must guide these efforts. We must ensure that we do not repeat the mistakes of history, such as the exploitation of natural resources and indigenous populations.
Moreover, scientific advancements have enabled us to develop technologies that enhance our understanding of the universe. Telescopes and space probes allow us to observe distant galaxies, study black holes, and uncover the mysteries of dark matter. Each discovery leads to new questions, further fueling our curiosity and drive for knowledge. The concept of the multiverse, for instance, challenges our understanding of reality and pushes the boundaries of scientific thought.
In addition to exploring the universe, science plays a crucial role in addressing pressing issues on Earth. Climate change, for example, is a significant concern that scientists are actively investigating. Through climate models and data analysis, researchers can predict future trends and propose solutions to mitigate the effects of global warming. Public awareness and education are essential in fostering a collective response to environmental challenges.
As we reflect on the wonders of science, it is clear that its contributions extend far beyond mere knowledge acquisition. Science empowers us to make informed decisions about our health, environment, and future. By fostering a culture of curiosity and critical thinking, we can inspire future generations to continue exploring the unknown.
Which of the following best summarises the passage?
Trong các hàm số dưới đây, hàm số nào nghịch biến trên \(\left( {0; + \infty } \right)\)?
Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the correct answer to each of the questions from 28 to 34. Foot-racing is a popular activity in the United States. It is seen not only as a competitive sport but also as a way to exercise, to enjoy the camaraderie of like-minded people, and to donate money to a good cause. Though serious runners may spend months training to compete, other runners and walkers might not train at all. Those not competing to win might run in an effort to beat their own time or simply to enjoy the fun and exercise. People of all ages, from those of less than one year (who may be pushed in strollers) to those in their eighties, enter into this sport. The races are held on city streets, on college campuses, through parks, and in suburban areas, and they are commonly 5 to 10 kilometers in length. The largest footrace in the world is the 12-kilometer Bay to Breakers race that is held in San Francisco every spring. This race begins on the east side of the city near San Francisco Bay and ends on the west side at the Pacific Ocean. There may be 80,000 or more people running in this race through the streets and hills of San Francisco. In the front are the serious runners who compete to win and who might finish in as little as 34 minutes. Behind them are the thousands who take several hours to finish. In the back of the race are those who dress in costumes and come just for fun. One year there was a group of men who dressed like Elvis Presley, and another group consisted of firefighters who were tied together in a long line and who were carrying a fire-hose. There was even a bridal party, in which the bride was dressed in a long white gown and the groom wore a tuxedo. The bride and groom threw flowers to bystanders, and they were actually married at some point along the route.
The word “camaraderie” as used in the first paragraph could be best replaced by which of the following?
Văn bản công nhận nền độc lập của 13 thuộc địa Anh ở Bắc Mĩ là
Ở vi khuẩn hô hấp hiếu khí, khi phân giải 1 phân tử glucôzơ thì chúng sẽ tích lũy được bao nhiêu phân tử ATP?
Văn minh Ấn Độ cổ - trung đại gắn liền với những dòng sông nào?
Etilen có vai trò ra sao?
Hai quả bóng có khối lượng \(m_1 = 6g, m_2 = 12g\) được ép sát vào nhau trên mặt bàn nằm ngang. Khi buông tay, hai quả lăn được các quãng đường lần lượt là \(s_1, s_2\) rồi dừng. Biết khi rời nhau, hai quả bóng chuyển động chậm dần cùng gia tốc. Tỉ số quãng đường của hai quả bóng chuyển động được là:
Bào quan nào sau đây chỉ có ở tế bào động vật mà không có ở tế bào thực vật?
Đáp án nào sau đây không phải là nghệ thuật độc đáo được sử dụng trong bài Thu điếu?
Phương án nào sau đây mô tả đúng nhất bản chất của việc số hóa hình ảnh?
- Phát biểu nào sau đây là đúng khi nói về công ngiệp 4.0?
Khi thả một vật trượt không vận tốc đầu trên mặt phẳng nghiêng có ma sát thì
Read the following passage about Preserving Today's Soundscapes for Future Generations and mark the letter A, B, C or D on your answer sheet to indicate the best answer to each of the following questions from 23 to 30.
Sonic time capsules save today's sounds for future people. Scientists capture everyday sounds like streets, birds, and children playing in parks around the world. These recordings help us remember our world before changes. Cities are losing unique sounds as life becomes similar everywhere. Old machines, music, and natural sounds might disappear if not saved. Many important cultural sounds are already lost forever because nobody thought to record them when they still existed.
Sound collectors use microphones to record in different places. They visit forests, oceans, cities, and villages to capture soundscapes throughout different seasons and times of day. They store sounds in digital libraries for years. Museums have rooms for listening to past sounds. These experiences help people understand history in ways books cannot. Some researchers travel to remote locations to record indigenous languages and traditional ceremonies before they vanish from our collective memory.
Climate change is changing world sounds. Melting glaciers, endangered animals, and disappearing languages need saving before they're gone. Researchers believe future people will want to know how our world sounded. These capsules will be important records, like photographs. Scientists study how sounds affect human health. The sounds of nature can reduce stress and improve mental health, which makes preserving natural soundscapes even more important for future generations who may live in highly urbanized environments.
Community projects invite people to record daily sounds. Children learn to listen carefully to the world around them and identify sounds that matter to their community. Old people share recordings from their childhood. People feel emotions when listening to these collections. Artists create music using everyday recordings. These projects help communities protect special sounds for the future. Some cities now have sound preservation policies that protect unique acoustic environments just as they would protect historic buildings or natural landscapes from development.
The word “they” in paragraph 2 refers to _________.
Chủ thể tiêu dùng có vai trò gì sau đây?
Choose A, B, C or D that has the CLOSEST meaning to the underlined word/phrase in each question.
Groundbreaking research in the field of quantum physics was conducted by Albert Einstein in the early 20th century.
Phát biểu nào sau đây không chính xác về môi trường sống của con người?