Properties of Triangle - Napier's Analogy

Duration: 2 min

This video lesson is available to enrolled students.

Return to /learn/COCUBES-PREPARATION/quantitative-aptitude/trigonometry/properties-of-triangle/asset-properties-of-triangle-napiers-analogy after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. Quantitative Aptitude: Number System, Divisibility Rules, HCF LCM, Percentage, Ratio and Proportion (Ratios), Average, Profit and Loss, Simple Interest and Compound Interest, Mixture and Alligation, Partnership, Age Problems, Time and Work, Pipe and Cistern, Speed Time and Distance, Algebra, Arithmetic, Data Interpretation, Sequence and Series (Series), Logarithm, Powers and Exponents (Surds and Indices), Permutation and Combination, Probability, Speed Mathematics and Basic Mathematics, Trigonometry
  2. Logical Reasoning: Coding Decoding, Blood Relations, Directions (Direction Test), Ranking, Order and Sequence, Seating Arrangements, Puzzle Solving (Puzzles), Data Arrangement, Syllogisms, Inequality, Data Sufficiency, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Series (Number and Letter Series) (Numerical Relations and Reasoning), Venn Diagram, Logical Sequence Of Words, Calendar, Clock, Cubes & Dices, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning)
  3. Verbal Ability: Noun, Pronoun, Adjectives, Verb, Adverb, Tenses, Subject Verb Agreement (Verb Noun Agreement), Articles, Preposition, Conjunction, Modals, Determiner, Vocabulary, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Active Passive Voice (Voice), Direct and Indirect Speech, Sentence Construction
  4. Data Structures (Domain Test): Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  5. Algorithms (Domain Test): Algorithm Analysis, Sorting Algorithms, Time Complexity Analysis, Greedy Algorithms
  6. OOPs (Domain Test): Object Oriented Programming (OOPS)
  7. DBMS (Domain Test): Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, ORDBMS, Database Security & Authorization, Query Processing & Optimization, Enhanced Data Models, Data Warehousing & Mining, Big Data Systems, NoSQL
  8. SQL (Domain Test): SQL
  9. Operating Systems (Domain Test): Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Windows OS, Linux OS, Security, Distributed Systems, Virtual Machines
  10. Computer Networks (Domain Test): Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics, Network Security, Mobile Technology, Cloud Computing and IoT, Cyber and Info Security
  11. Coding: Coding Questions by Yash Sir, C Programming by Yash Sir, Programming in C++, Java, Python for Placements by Yash Sir
  12. Written English Test: English Writing Ability
  13. Psychometric Test: Behavioral Assessment (Behavioral Competency Profiling) (Psychometric Test)
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The video presents a lecture on Napier's Analogy, a set of trigonometric identities for triangles. The instructor begins by writing the title and the first formula, tan(B-C) = (b-c)/(b+c) * cot(A/2), on a digital blackboard. He then proceeds to write the analogous formulas for the other two angles, tan(C-A) and tan(A-B), using a standard triangle notation where angles A, B, C are opposite sides a, b, c respectively. The lecture progresses by drawing a triangle and labeling its vertices and sides. The instructor then fills in the complete set of three formulas, showing the pattern: for any two angles, the tangent of their difference is equal to the ratio of the difference of their opposite sides to the sum of those sides, multiplied by the cotangent of half the third angle. The final formulas are presented as a complete set, demonstrating the symmetry of Napier's Analogies.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a digital blackboard displaying the title 'Napier's Analogy :'. The instructor writes the first formula: tan(B-C) = (b-c)/(b+c) * cot(A/2). He then writes the second formula, tan(C-A) = (c-a)/(c+a) * cot(B/2), and the third, tan(A-B) = (a-b)/(a+b) * cot(C/2). As he writes, a diagram of a triangle with vertices A, B, C and opposite sides a, b, c is drawn on the right side of the screen. The instructor uses a yellow pen to write the formulas and draw the triangle, and a white pen for the final formulas. The 'KNOWLEDGE GATE' logo is visible in the bottom right corner.

  2. 2:00 – 2:20 02:00-02:20

    The instructor completes the set of Napier's Analogies on the screen. The final formulas are clearly displayed: tan(B-C) = (b-c)/(b+c) * cot(A/2), tan(C-A) = (c-a)/(c+a) * cot(B/2), and tan(A-B) = (a-b)/(a+b) * cot(C/2). The triangle diagram with labeled vertices and sides remains on the right. The instructor has used a yellow pen for the initial writing and a white pen for the final, complete set of formulas, which are now fully visible. The 'KNOWLEDGE GATE' logo is still present in the bottom right corner.

The video systematically presents Napier's Analogies, a fundamental set of trigonometric identities for any triangle. The core concept is the relationship between the tangent of the difference of two angles and the ratio of the difference and sum of their opposite sides, scaled by the cotangent of half the third angle. The lecture follows a clear progression: it introduces the topic, presents the first formula, then derives the other two by analogy, and finally displays the complete, symmetric set of three identities. The use of a standard triangle diagram (A, B, C opposite a, b, c) is crucial for understanding the pattern and application of these formulas.

Loading lesson…