Chapter Formula Poster (One Page)

ROLE: Act as an experienced mathematics teacher and exam-revision specialist.

CONTEXT: I teach [CLASS/GRADE] students for the [BOARD or EXAM e.g. CBSE / ICSE / State Board / JEE / NEET]. I need a single-page formula poster for the chapter [CHAPTER NAME e.g. Trigonometry]. The students are revising, so it must be complete, correct, and easy to scan.

YOUR TASK:
1. List EVERY important formula, identity, and standard result from this chapter for this class and board.
2. Group the formulas under clear sub-headings (for example: Basic Definitions, Identities, Standard Results, Special Cases).
3. Order them in the same sequence the textbook teaches them.
4. For each formula, write it once, cleanly, with correct symbols.
5. Keep the total length to what fits on ONE printed A4 page.

INPUT: Here is the chapter and class. Chapter: [PASTE CHAPTER NAME HERE]. Class/Board: [PASTE HERE]. If I paste a list of topics or a syllabus, use only those topics.

HOW TO WORK IT OUT: First, recall the standard syllabus for this chapter and this board. Solve or derive nothing aloud, but internally confirm each formula is the standard, correct version. VERIFY the final sheet two ways: (a) re-read every formula and check each symbol, sign, and power is correct; (b) check no major formula from this chapter is missing by comparing against the usual textbook table of contents for the chapter. Never invent a formula or a value. Keep all maths fully legible using clean plain text or simple LaTeX, so it copies correctly into a document.

OUTPUT FORMAT (use exactly this order):
1. TITLE LINE: '[Chapter Name] - Formula Sheet (Class [X], [Board])'.
2. A line: 'Compiled by [YOUR NAME]'.
3. The grouped formulas under sub-headings, each formula on its own line and numbered.
4. A short 'Quick Notes' box at the end with 3 to 5 one-line reminders.
5. A footer line.

RULES: Be complete but tight - no examples, no derivations, no explanations unless asked. Every formula must be exam-accurate. Use consistent notation throughout.

OUTPUT FILE FORMAT: present the complete result as a clean, ready-to-use document I can paste straight into Microsoft Word or Google Docs - a clear bold title, section headings, neatly numbered items, comfortable spacing, and simple tables only where helpful (avoid heavy formatting that breaks on paste). It must also print cleanly to PDF on A4 (File > Print > Save as PDF). Keep all mathematics fully readable (fractions as a/b, powers as x^2, roots as sqrt(x)).

MATHS FORMATTING: Write ALL mathematics so it reads correctly in a normal chat and pastes cleanly into Word or Google Docs. Use plain readable notation - for example a/b for fractions, x^2 for powers, sqrt(x) for roots, and symbols like <=, >=, !=, +-, pi, theta, integral and sum. Do NOT output raw LaTeX or code such as \frac{}{}, \sqrt{}, x^{2}, $...$ or \( ... \) - these appear as broken symbols to a teacher in a free chat.

CONTEXT CHECK: Before you begin, if any [SQUARE-BRACKET] above is still empty, or I have not given you the question / photo / data you need, ask me for exactly those and wait - never guess, and never answer with the placeholder text still in brackets.

GROUND RULES (always follow): Do not invent statistics, percentages, marks distributions you were not given, exam cut-offs, solve-time figures, NCERT or textbook page/line numbers, citations, or historical exam data. If you are unsure of any fact or number, say so and clearly label it an estimate; keep established fact separate from your own inference. Every step must be mathematically correct and at the stated class/board/exam level.

SIGNATURE: End your ENTIRE response with exactly this footer block (keep the lines and symbols):
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Questions, feedback or appreciation are always welcome.
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