RS Aggarwal Class 12 Solutions Chapter 4

1. What is an inverse trigonometric function, and how does it work?

Ans – Inverse trigonometry is the opposite of the basic trigonometric functions, such as sine, cosine, tangent, cotangent, etc. They are also called the arc functions, anti trigonometric functions, and cyclometric functions. When you do the opposite of trigonometric functions, you get the length of the arc that is needed to get the value you want.

With the help of trigonometric ratios, these functions are used to find the angles. In the fields of physics and navigation, these functions are used all the time. When you know the lengths of two sides of a right triangle, you can use the six important functions to find the lengths of the angles.

2. What are all six inverse trigonometric functions and formulas?

Ans – Arcsine, Arccosine, Arctangent, Arccotangent, Arcsecant, and Arccosecant are the six inverse trigonometric identities or functions. These functions are used a lot in engineering, physics, geometry, and other fields.

Here are the main formulas for inverse trigonometry:

• Arcsine : sin^-1(-x) = -sin^-1(x), x ∈ [-1, 1]
• Arccosine : cos^-1(-x) = π -cos^-1(x), x ∈ [-1, 1]
• Arctangent : tan^-1(-x) = -tan^-1(x), x ∈ R
• Arccotangent : cot^-1(-x) = π – cot^-1(x), x ∈ R
• Arcsecant : sec^-1(-x) = π -sec^-1(x), |x| ≥ 1
• Arccosecant : cosec^-1(-x) = -cosec^-1(x), |x| ≥ 1

3. From where I can download RS Aggrawal Class 12 solutions Chapter 4 ?

Ans –  Students can get RS Aggarwal Class 12 Solutions Chapter 4 Trigonometric functions from the Utopper website or app. The experts who put together these solutions for Class 12 Mathematics know a lot about the subject and can help students prepare better for their exams.

4. How many exercises are in RS Aggrawal Class 12 Solutions Chapter 4?

Ans – This chapter is longer than the ones that came before it in RS Aggarwal Class 12 Solutions Chapter 4. In Chapter 4 of Class 12 Math, “Inverse of Trigonometric Functions,” there are a total of 126 questions spread across 5 exercises. These questions are meant to help students fully understand the chapter’s ideas and review what they’ve learned. In the first set of exercises, students learn about the values of inverse trigonometric functions. In later exercises, they learn about different proofs and properties of inverse trigonometric functions. 

5. What are the Identities of Inverse Trigonometric Function ?

Ans – Inverse trigonometric functions have the following :

• sin-1 (sin x) = x provided –π/2 ≤ x ≤ π/2
• cos-1 (cos x) = x provided 0 ≤ x ≤ π
• tan-1 (tan x) = x provided –π/2 < x < π/2
• sin(sin-1 x) = x provided -1 ≤ x ≤ 1
• cos(cos-1 x) = x provided -1 ≤ x ≤ 1
• tan(tan-1 x) = x provided x ∈ R
• cosec(cosec-1 x) = x provided -1 ≤ x ≤ ∞ or -∞ < x ≤ 1
• sec(sec-1 x) = x provided 1 ≤ x ≤ ∞ or -∞ < x ≤ 1
• cot(cot-1 x) = x provided -∞ < x < ∞
• sin^(-1) = (2x)/(1 + x^2) = 2 tan^{-1}x
• cos^(-1) = (1 – x^2)/(1 + x^2) = 2 tan^{-1}x
• tan^(-1) = (2x)/(1 – x^2) = 2 tan^{-1}x
• 2cos-1 x = cos-1 (2×2 – 1)
• 2sin-1x = sin-1 2x√(1 – x2)
• 3sin-1x = sin-1(3x – 4×3)
• 3cos-1 x = cos-1 (4×3 – 3x)
• 3tan-1x = tan-1((3x – x3/1 – 3×2))
• sin-1x + sin-1y = sin-1{ x√(1 – y2) + y√(1 – x2)}
• sin-1x – sin-1y = sin-1{ x√(1 – y2) – y√(1 – x2)}
• cos-1 x + cos-1 y = cos-1 [xy – √{(1 – x2)(1 – y2)}]
• cos-1 x – cos-1 y = cos-1 [xy + √{(1 – x2)(1 – y2)}
• tan-1 x + tan-1 y = tan-1(x + y/1 – xy)
• tan-1 x – tan-1 y = tan-1(x – y/1 + xy)
• tan-1 x + tan-1 y +tan-1 z = tan-1 (x + y + z – xyz)/(1 – xy – yz – zx)