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Trigonometric Functions - II

NIOS · Class 12 · Mathematics

Quick revision notes for Trigonometric Functions - II — NIOS Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

45 questions25 flashcards5 concepts

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A two-part infographic summarizing the transformation formulas: converting products of trigonometric functions into sums or differences, and converting sums or differences into products.
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Key Topics to Revise

1

Addition and Subtraction Formulae

  • cos(A+B) = cosA cosB - sinA sinB — this is the MASTER formula from which all others are derived
  • cos(A-B) = cosA cosB + sinA sinB — replace B with -B in cos(A+B)
  • sin(A+B) = sinA cosB + cosA sinB — derived using complementary angle identity
2

Product-to-Sum and Sum-to-Product Transformations

  • These formulae convert products of trig functions into sums/differences and vice versa
  • Product-to-Sum: 2sinAcosB = sin(A+B) + sin(A−B)
  • Product-to-Sum: 2cosAsinB = sin(A+B) − sin(A−B)
3

Multiple Angle Formulae (2A and 3A)

  • sin2A = 2sinAcosA = 2tanA/(1+tan²A)
  • cos2A = cos²A − sin²A = 2cos²A − 1 = 1 − 2sin²A = (1−tan²A)/(1+tan²A)
  • tan2A = 2tanA/(1−tan²A)
4

Sub-Multiple Angle Formulae (A/2)

  • A/2, A/3, A/4 are called sub-multiples of A
  • sin(A/2) = ±√((1−cosA)/2) — sign depends on the quadrant of A/2
  • cos(A/2) = ±√((1+cosA)/2) — sign depends on the quadrant of A/2

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Full Notes

Key Concepts

These are fundamental formulae that expressThese formulae convert products of trigonometricThe reverse transformation converts sumsThese formulae express trigonometric functionsThese formulae express trigonometric functions

Frequently Asked Questions

What are the important topics in Trigonometric Functions - II for NIOS Class 12 Mathematics?
Key topics in Trigonometric Functions - II include Complete Overview: Trigonometric Functions II, Trigonometric Functions - II: Complete Concept Map, Mind map showing all major topics covered in the chapter with their key subtopics. These are the concepts NIOS Class 12 examiners draw on most — study them first, then practise related questions.
How to score full marks in Trigonometric Functions - II — NIOS Class 12 Mathematics?
Understand the core concepts first, then work through the 45 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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