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Trigonometric Functions - II — Revision Notes

NIOS · Class 12 · Mathematics

Trigonometric Functions - II revision notes for NIOS Class 12 Mathematics: 4 topics in quick points. Part of the NIOS Class 12 Mathematics syllabus.

45 questions25 flashcards7 formulas & key relations5 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 Addition and Subtraction Formulae, Product-to-Sum and Sum-to-Product Transformations, Multiple Angle Formulae (2A and 3A), Sub-Multiple Angle Formulae (A/2). Study these first, then practise questions on each for the NIOS Class 12 board exam.
How should I revise Trigonometric Functions - II for the NIOS Class 12 board exam?
Learn the core ideas first, then work through the 45 practice questions on Trigonometric Functions - II. Revise 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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All NIOS Class 12 Mathematics Revision Notes

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