NCERT Solutions for Class 12 Maths Chapter 2 – Inverse Trigonometric Functions Exercise 2.1

Flashcard for Question 1

Short Formula Recall:
sin⁻¹(x) principal range = [−π/2, π/2]

Quick Tip:
Find the reference angle for 1/2, then apply the negative sign and ensure it lies in [−π/2, π/2].

Common Mistake:
Giving a positive angle or forgetting to stay within the principal value range.

Exam Insight:
A standard 1-mark question checking understanding of principal value ranges of inverse trigonometric functions.

Flashcard for Question 2

Short Formula Recall:
cos⁻¹(x) principal range = [0, π]

Quick Tip:
Identify the reference angle for √3/2 and ensure it lies in [0, π].

Common Mistake:
Confusing cos⁻¹ with sin⁻¹ range and giving an answer outside [0, π].

Exam Insight:
Common 1-mark board question to test quick recall of standard angles in inverse cosine.

Flashcard for Question 3

Short Formula Recall:
cosec⁻¹(x) principal range = [−π/2, 0) ∪ (0, π/2]

Quick Tip:
Take reciprocal to convert to sin⁻¹(1/2) and then find the value within the principal range of cosec⁻¹.

Common Mistake:
Forgetting to take reciprocal first or giving a value outside the allowed range.

Exam Insight:
Often used to test knowledge of reciprocal inverse trigonometric function relationships.

Flashcard for Question 4

Short Formula Recall:
tan⁻¹(x) principal range = (−π/2, π/2)

Quick Tip:
Find the reference angle for √3 and apply the negative sign, ensuring the result lies in (−π/2, π/2).

Flashcard for Question 7

Short Formula Recall:
sec⁻¹(x) principal range = [0, π] \ {π/2}

Quick Tip:
Take reciprocal to convert to cos⁻¹(√3/2) and then ensure the answer lies within the principal range of sec⁻¹.

Common Mistake:
Not taking the reciprocal first or giving an angle where cos is undefined (π/2).

Flashcard for Question 8

Short Formula Recall:
cot⁻¹(x) principal range = (0, π)

Quick Tip:
Identify the angle whose cot value is √3 and ensure it lies between 0 and π.

Common Mistake:
Confusing cot⁻¹ with tan⁻¹ range or giving a negative angle.

Flashcard for Question 11

Quick Tip:
Evaluate each inverse trig function separately using standard angles, then sum the results.

Common Mistake:
Mixing up the principal value ranges or forgetting negative signs in sine values.

Exam Insight:
Tests ability to handle multiple inverse trig functions together — often appears as a 2–3 mark calculation problem.