CBSE Class 12 Maths Notes Chapter 2: Chapter 2 of CBSE Class 12 Maths is about Inverse Trigonometric Functions. This chapter talks about the inverse of basic trigonometric functions like sine, cosine, and tangent. Essentially, it is about reversing these functions to find angles when you know the trigonometric values.
The chapter explains the range and domain of these inverse functions, showing what values are valid and how to use them. You’ll learn how to solve problems where you need to find angles from given trigonometric expressions. The notes include simple steps and examples to help you understand and practice these concepts making it easier to solve related problems in exams.CBSE Class 12 Maths Notes Chapter 2 PDF
Function Name | Notation | Definition | Domain of x | Range |
Arcsine or inverse sine | y = sin -1 (x) | x = sin y | −1 ≤ x ≤ 1 i.e. [-1, 1] |
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Arccosine or inverse cosine | y = cos -1 (x) | x = cos y | −1 ≤ x ≤ 1 i.e. [-1, 1] |
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Arctangent or Inverse tangent | y = tan -1 (x) | x = tan y | For all real numbers |
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Arccotangent or Inverse Cot | y = cot -1 (x) | x = cot y | For all real numbers |
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Arcsecant or Inverse Secant | y = sec -1 (x) | x = sec y | x ≤ −1 or 1 ≤ x R – (-1, 1) |
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Arccosecant | y = csc -1 (x) | x = csc y | x ≤ −1 or 1 ≤ x R – (-1, 1) |
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Set 1:
sin −1 (1/x) = cosec −1 x, x ≥ 1 or x ≤ −1 cos −1 (1/x) = sec −1 x, x ≥ 1 or x ≤ −1 tan −1 (1/x) = cot –1 x, x > 0Set 2:
(i) sin –1 (–x) = – sin –1 x, x ∈ [– 1, 1] (ii) tan –1 (–x) = – tan –1 x, x ∈ R (iii) cosec –1 (–x) = – cosec –1 x, | x | ≥ 1Set 3:
(i) cos –1 (–x) = π – cos –1 x, x ∈ [– 1, 1] (ii) sec –1 (–x) = π – sec –1 x, | x | ≥ 1 (iii) cot –1 (–x) = π – cot –1 x, x ∈ RSet 4:
(i) sin –1 x + cos –1 x = π/2, x ∈ [– 1, 1] (ii) tan –1 x + cot –1 x = π/2, x ∈ R (iii) cosec –1 x + sec –1 x = π/2, |x| ≥ 1Set 5:
Set 6:
1. y= sin-1(x)
y= cos-1(x)
2. y = tan-1(x)
3. y= cot-1(x)
4. y = cosec-1(x)
5. y= sec-1(x)
NOTE:
sin-1(x) and tan-1(x) are increasing functions, whereas cos-1(x) and cot-1(x) are decreasing functions over their domain. sin-1(x) and (sin (x))-1 are different and should not be confused.