January 13, 2024

Comprehensive solutions for Class 12 Science Mathematics Chapter 2, Inverse Trigonometric Functions, are available here, complete with straightforward step-by-step explanations. Widely favored among Class 12 Science students, these solutions for Inverse Trigonometric Functions in Mathematics prove invaluable for efficiently completing homework assignments and preparing for exams. All queries and their corresponding answers from Chapter 2 of the NCERT Book for Class 12 Science Mathematics are generously provided on this platform, completely free of charge. Page No 41: Question 1: Find the principal value of  ANSWER: Let sin-1  Then sin y =  We know that the range of the principal value branch of sin−1 is and sin Therefore, the principal value of  Page No 41: Question 2: Find the principal value of  ANSWER: We know that the range of the principal value branch of cos−1 is . Therefore, the principal value of. Page No 41: Question 3: Find the principal value of cosec−1 (2) ANSWER: Let cosec−1 (2) = y. Then,  We know that the range of the principal value branch of cosec−1 is  Therefore, the principal value of  Page No 41: Question 4: Find the principal value of  ANSWER: We know that the range of the principal value branch of tan−1 is  Therefore, the principal value of  Page No 41: Question 5: Find the principal value of  ANSWER: We know that the range of the principal value branch of cos−1 is Therefore, the principal value of  Page No 41: Question 6: Find the principal value of tan−1 (−1) ANSWER: Let tan−1 (−1) = y. Then,  We know that the range of the principal value branch of tan−1 is Therefore, the principal value of  Page No 42: Question 7: Find the principal value of  ANSWER: We know that the range of the principal value branch of sec−1 is Therefore, the principal value of  Page No 42: Question 8: Find the principal value of  ANSWER: We know that the range of the principal value branch of cot−1 is (0,π) and Therefore, the principal value of  Page No 42: Question 9: Find the principal value of  ANSWER: We know that the range of the principal value branch of cos−1 is [0,π] and . Therefore, the principal value of  Page No 42: Question 9: Find the principal value of  ANSWER: We know that the range of the principal value branch of cos−1 is [0,π] and . Therefore, the principal value of  Page No 42: Question 10: Find the principal value of  ANSWER: We know that the range of the principal value branch of cosec−1 is  Therefore, the principal value of  Page No 42: Question 11: Find the value of  ANSWER: Page No 42: Question 12: Find the value of  ANSWER: Page No 42: Question 13: Find the value of if sin−1x = y, then (A) (B)  (C) (D)  ANSWER: It is given that sin−1x = y. We know that the range of the principal value branch of sin−1 is  Therefore,. Page No 42: Question 14: Find the value of is equal to (A) π (B)  (C)  (D)  ANSWER: Page No 47: Question 1: Prove  ANSWER: To prove:  Let x = sinθ. Then,  We have, R.H.S. = = 3θ = L.H.S. Page No 47: Question 2: Prove  ANSWER: To prove: Let x = cosθ. Then, cos−1x =θ. We have, Page No 47: Question 3: Prove  ANSWER: To prove: Page No 47: Question 4: Prove  ANSWER: To prove:  Page No 47: Question 5: Write the function in the simplest form: ANSWER: Page No 47: Question 6: Write the function in the simplest form: ANSWER: Put x = cosec θ ⇒ θ = cosec−1x Page No 47: Question 7: Write the function in the simplest form: ANSWER: Page No 47: Question 8: Write the function in the simplest form: ANSWER: Page No 48: Question 9: Write the function in the simplest form: ANSWER: Page No 48: Question 10: Write the function in the simplest form: ANSWER: Page No 48: Question 11: Find the value of  ANSWER: Let. Then, Page No 48: Question 12: Find the value of  ANSWER: Page No 48: Question 13: Find the value of  ANSWER: Let x = tan θ. Then, θ = tan−1x. Let y = tan Φ. Then, Φ = tan−1y. Page No 48: Question 14: If, then find the value of x. ANSWER: On squaring both sides, we get: Hence, the value of x is Page No 48: Question 15: If, then find the value of x. ANSWER: Page No 48: Question 16: Find the values of  ANSWER: We know that sin−1 (sin x) = x if, which is the principal value branch of sin−1x. Here, Now, can be written as: Page No 48: Question 17: Find the values of  ANSWER: We know that tan−1 (tan x) = x if, which is the principal value branch of tan−1x. Here, Now, can be written as: Page No 48: Question 18: Find the values of  ANSWER: Let. Then, Page No 48: Question 19: Find the values of is equal to (A) (B) (C) (D)  ANSWER: We know that cos−1 (cos x) = x if, which is the principal value branch of cos −1x. Here, Now, can be written as: The correct answer is B. Page No 48: Question 20: Find the values of is equal to (A) (B) (C) (D) 1 ANSWER: Let. Then,  We know that the range of the principal value branch of. ∴ The correct answer is D. Page No 48: Question 21: Find the values of is equal to (A) π (B) (C) 0 (D)  ANSWER: Let. Then, We know that the range of the principal value branch of Let. The range of the principal value branch of The correct answer is B. Page No 51: Question 1: Find the value of  ANSWER: We know that cos−1 (cos x) = x if, which is the principal value branch of cos −1x. Here, Now, can be written as: Page No 51: Question 2: Find the value of  ANSWER: We know that tan−1 (tan x) = x if, which is the principal value branch of tan −1x. Here, Now, can be written as: Page No 51: Question 3: Prove  ANSWER: Now, we have: Page No 51: Question 4: Prove  ANSWER: Now, we have: Page No 51: Question 5: Prove  ANSWER: Now, we will prove that: Page No 51: Question 6: Prove  ANSWER: Now, we have: Page No 51: Question 7: Prove  ANSWER: Using (1) and (2), we have Page No 51: Question 8: Prove  ANSWER: Page No 52: Question 9: Prove  ANSWER: Page No 52: Question 10: Prove  ANSWER: Page No 52: Question 11: Prove  [Hint: putx = cos 2θ] ANSWER: Page No 52: Question 12: Prove  ANSWER: Page No 52: Question 13: Solve ANSWER: Page No 52: Question 14: Solve ANSWER: Page No 52: Question 15: Solveis equal to (A)  (B)  (C)  (D)  …

NCERT Solutions for Class 12 Science Maths Chapter 2 – Inverse Trigonometric Functions Read More »