Chapter 2 - Principal Values of Inverse Trigonometric Functions
Overview
This page provides comprehensive Class 12 Maths Chapter 2 Principal Values. Chapter 2 - Principal Values of Inverse Trigonometric Functions - Free study material for Class 12 Maths. NCERT Solutions, Notes, and PYQs.
Class 12 Mathematics | Previous Year Questions
Q1
2020
00:00
The principal value of tan⁻¹(√3) is
We know that tan(π/3) = √3.
The principal value range of tan⁻¹x is (−π/2, π/2).
Since π/3 lies in (−π/2, π/2), it is the principal value.
π/3
Q2
2020
00:00
The principal value of cos⁻¹(−1/2) is
We know that cos(2π/3) = −1/2.
The principal value range of cos⁻¹x is [0, π].
Since 2π/3 lies in [0, π], it is the principal value.
2π/3
Q3
2021
00:00
The principal value of sin⁻¹(−√3/2) is
We know that sin(−π/3) = −√3/2.
The principal value range of sin⁻¹x is [−π/2, π/2].
Since −π/3 lies in this interval, it is the principal value.
−π/3
Q4
2022
00:00
Find the principal value of sec⁻¹(2).
sec⁻¹x is defined in the range [0, π], x ≠ π/2.
sec(π/3) = 2.
Hence, the principal value is π/3.
π/3
Q5
2023
00:00
The principal value of cot⁻¹(−1) is
The principal value range of cot⁻¹x is (0, π).
cot(3π/4) = −1.
Since 3π/4 lies in (0, π), it is the principal value.
3π/4
Q6
2024
00:00
The principal value of tan⁻¹(−1) is
We know that tan(−π/4) = −1.
The principal value range of tan⁻¹x is (−π/2, π/2).
Since −π/4 lies in this interval, it is the principal value.
−π/4
Q7
2020
00:00
The principal value of cos⁻¹(1/2) is
We know that cos(π/3) = 1/2.
The principal value range of cos⁻¹x is [0, π].
Since π/3 lies in this interval, it is the principal value.
π/3
Q8
2020
00:00
The principal value of sin⁻¹(1) is
We know that sin(π/2) = 1.
The principal value range of sin⁻¹x is [−π/2, π/2].
Hence, the principal value is π/2.
π/2
Q9
2021
00:00
Find the principal value of cot⁻¹(√3).
The principal value range of cot⁻¹x is (0, π).
cot(π/6) = √3.
Since π/6 lies in (0, π), it is the principal value.
π/6
Q10
2022
00:00
The principal value of sec⁻¹(−2) is
The principal value range of sec⁻¹x is [0, π], x ≠ π/2.
sec(2π/3) = −2.
Since 2π/3 lies in [0, π], it is the principal value.
2π/3
Q11
2023
00:00
The principal value of tan⁻¹(0) is
We know that tan(0) = 0.
The principal value range of tan⁻¹x is (−π/2, π/2).
Hence, the principal value is 0.
0
Q12
2024
00:00
The principal value of sin⁻¹(−1/2) is
We know that sin(−π/6) = −1/2.
The principal value range of sin⁻¹x is [−π/2, π/2].
Since −π/6 lies in this interval, it is the principal value.
−π/6
Q13
2021
00:00
The principal value of cos⁻¹(0) is
We know that cos(π/2) = 0.
The principal value range of cos⁻¹x is [0, π].
Since π/2 lies in [0, π], it is the principal value.
π/2
Q14
2022
00:00
Find the principal value of tan⁻¹(1/√3).
We know that tan(π/6) = 1/√3.
The principal value range of tan⁻¹x is (−π/2, π/2).
Since π/6 lies in this interval, it is the principal value.
π/6
Q15
2023
00:00
The principal value of cosec⁻¹(−2) is
The principal value range of cosec⁻¹x is [−π/2, 0) ∪ (0, π/2].
cosec(−π/6) = −2.
Since −π/6 lies in the principal value range, it is the principal value.
−π/6
Q16
2024
00:00
Assertion (A): The principal value of sin⁻¹(1/2) is π/6. Reason (R): The range of sin⁻¹x is [−π/2, π/2].
We know that sin(π/6) = 1/2.
The principal value range of sin⁻¹x is [−π/2, π/2].
Since π/6 lies in this range, sin⁻¹(1/2) = π/6.
Thus, both the Assertion and Reason are true and Reason correctly explains the Assertion.
Both A and R are true and R is the correct explanation of A.