Maths Inverse Trigonometric Functions Formulas: Calculus is one of the most important topics in mathematics. The CBSE Class 11 and 12 introduce students to many advanced concepts in calculus. Nearly half the curriculum of Class 12 is composed of calculus, and students need to be proficient in it to score well in the board exams.
There are many ways to learn and apply mathematics. Due to the vastness of the subject, mathematicians have devised formulas to simplify equations and complex theories. Students are also taught many formulas in CBSE Class 12, especially in calculus chapters like Inverse Trigonometric Functions.
Formulas, theorems and other maths rules help simplify equations and problems and solve them quickly. Not using them makes some maths problems infinitely difficult, as you’ll notice in your class 12 studies.
Here at Jagran Josh, we cover the list of all important formulas, definitions, and glossaries of Inverse Trigonometric Functions, along with necessary examples. You can check the CBSE Class 12 Maths Chapter 2 Inverse Trigonometric Functions Formulas below.
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CBSE Class 12 Maths Chapter 2 Inverse Trigonometric Functions Formulas and Theorems
We have listed all the important formulas of CBSE Class 12 Inverse Trigonometric Functions here.
- The value of an inverse trigonometric function which lies in its principal value branch is called the principal value of that inverse trigonometric functions.
- The domains and ranges (principal value branches) of inverse trigonometric functions:
Other Formulas for CBSE Class 12 Inverse Trigonometric Functions:
sin-1x = - sin-1x
cos-1x = π - cos-1x
tan-1(-x) = -tan-1x
cosec⁻¹(-x) = -cosec⁻¹x
sec-1(-x) = π - sec-1x
cot-1(-x) = π - cot-1x
sin-1x + cos-1x = π/2
tan-1x + cot-1x = π/2
sec-1x + cosec-1x = π/2
sin-1(1/x) = cosec-1x, if x ≥ 1 or x ≤ -1
cos-1(1/x) = sec-1x, if x ≥ 1 or x ≤ -1
tan-1(1/x) = cot-1x, x > 0
sin-1x + cos-1x = π/2, x ∈ [-1,1]
tan-1x + cot-1x = π/2, x ∈ R
sec-1x + cosec-1x = π/2, x ∈ R - [-1,1]
Double Of Inverse Trigonometric Functions
2tan-1x = sin-1(2x/1+ x2)
= cos-1(1-x2/1+x2)
= tan-1(2x/1-x2)
2sin-1x = sin-1(2x.√(1 - x2))
2cos-1x = cos-1(2x2 - 1)
Triple Of Inverse Trigonometric Functions
3sin-1x = sin-1(3x - 4x3)
3cos-1x = cos-1(4x3 - 3x)
3tan-1x = tan-1(3x - x3/1 - 3x2)