Complete, verified solutions to the NCERT Class 12 Maths Chapter 2 (Inverse Trigonometric Functions) exercise questions. These Class 12 Mathematics Chapter 2 solutions are also useful as quick revision notes before exams.
NCERT Exercise Solutions
2.1 Find the principal value of sin⁻¹(−1/2).
Ans: sin⁻¹(−1/2) = −π/6, since sin(−π/6) = −1/2 and −π/6 lies in the principal value range [−π/2, π/2].
2.2 Find the principal value of cos⁻¹(√3/2).
Ans: cos⁻¹(√3/2) = π/6, since cos(π/6) = √3/2 and π/6 lies in [0, π].
2.3 Find the principal value of cosec⁻¹(2).
Ans: cosec⁻¹(2) = π/6, since cosec(π/6) = 2.
2.4 Find the principal value of tan⁻¹(−√3).
Ans: tan⁻¹(−√3) = −π/3, since tan(−π/3) = −√3.
2.5 Find the principal value of cos⁻¹(−1/2).
Ans: cos⁻¹(−1/2) = 2π/3, since cos(2π/3) = −1/2 and 2π/3 ∈ [0, π].
2.6 Find the principal value of tan⁻¹(−1).
Ans: tan⁻¹(−1) = −π/4.
2.7 Find the principal value of sec⁻¹(2/√3).
Ans: sec⁻¹(2/√3) = π/6, since sec(π/6) = 2/√3.
2.8 Find the value of tan⁻¹(1) + cos⁻¹(−1/2) + sin⁻¹(−1/2).
Ans: π/4 + 2π/3 + (−π/6) = 3π/12 + 8π/12 − 2π/12 = 9π/12 = 3π/4.
2.9 Find the value of cos⁻¹(1/2) + 2sin⁻¹(1/2).
Ans: π/3 + 2(π/6) = π/3 + π/3 = 2π/3.
2.10 Find the value of tan⁻¹(√3) − sec⁻¹(−2).
Ans: π/3 − 2π/3 = −π/3 (using sec⁻¹(−2) = π − sec⁻¹(2) = π − π/3 = 2π/3).
2.11 Find the value of tan⁻¹(1) + tan⁻¹(0).
Ans: π/4 + 0 = π/4.
Class 12 Mathematics Chapter 2 – Notes and Extra Questions
Along with these NCERT Solutions, students can also use the Class 12 Mathematics Chapter 2 Extra Questions and Class 12 Mathematics Chapter 2 Revision Notes for quick revision and extra practice.
