Solve all your doubts with Teachoo Black (new monthly pack available now!)

Formulae based

Inverse Trigonometry Formulas

Example 3 (i) Important Deleted for CBSE Board 2023 Exams

Ex 2.2,1 Deleted for CBSE Board 2023 Exams

Ex 2.2, 2 Important Deleted for CBSE Board 2023 Exams

Example 8 Deleted for CBSE Board 2023 Exams

Ex 2.2, 12 Important Deleted for CBSE Board 2023 Exams

Ex 2.2, 14 Important Deleted for CBSE Board 2023 Exams

Example 4 Deleted for CBSE Board 2023 Exams

Ex 2.2, 3 Deleted for CBSE Board 2023 Exams

Misc. 8 Important Deleted for CBSE Board 2023 Exams

Ex 2.2, 4 Important Deleted for CBSE Board 2023 Exams

Ex 2.2, 15 Important Deleted for CBSE Board 2023 Exams

Example 13 Important Deleted for CBSE Board 2023 Exams

Misc. 14 Deleted for CBSE Board 2023 Exams

Misc 17 (MCQ) Deleted for CBSE Board 2023 Exams

Misc. 13 Important Deleted for CBSE Board 2023 Exams

Example 10 Important Deleted for CBSE Board 2023 Exams

Misc. 3 Deleted for CBSE Board 2023 Exams

Misc. 4 Important Deleted for CBSE Board 2023 Exams

Misc 12 Important Deleted for CBSE Board 2023 Exams

Misc 16 (MCQ) Important Deleted for CBSE Board 2023 Exams You are here

Last updated at Aug. 9, 2021 by Teachoo

Misc 16 Solve sin−1(1 – x) – 2sin−1 x = π/2 , then x is equal to (A) 0, 1/2 (B) 1, 1/2 (C) 0 (D) 1/2 sin−1 (1 – x) – 2sin−1 x = π/2 –2sin−1 x = 𝝅/𝟐 – sin−1 (1 – x) − 2sin−1 x = cos−1 (1 – x) We know that sin−1 x + cos−1x = 𝝅/𝟐 Replace x by (1 − x) sin-1 (1 − x) + cos−1 (1 − x) = 𝜋/2 cos-1 (1 − x) = 𝜋/2 – sin−1 (1 − x) Let sin−1 x = a, Hence our equation becomes −2a = cos−1 (1 – x) cos (−2a) = 1 – x cos (2a) = (1 – x) 1 – 2 sin2 a = 1 – x We assumed that sin−1 x = a 1 – 2 [sin(sin−1 x)]2 = 1 – x 1 – 2x2 = 1 – x 1 – 2x2 – 1 + x = 0 1 – 1 – 2x2 + x = 0 –2x2 + x = 0 0 = 2x2 – x 2x2 – x = 0 x (2x – 1) = 0 So, x = 0 and x = 1/2 But x = 𝟏/𝟐 does not satisfy the equation Taking equation sin−1(1 – x) – 2sin−1 x = π/2 Putting x = 𝟏/𝟐 in L.H.S sin−1(1− 1/2) – 2 sin−1 (1/2) = sin−1(1/2) – 2 sin−1 (1/2) = 𝜋/6 – 2 × 𝜋/6 = (𝜋 − 2𝜋)/6 = (− 𝜋)/6 ≠ 𝝅/𝟐 Hence x = 1/2 not possible ∴ x = 0 is the only solution Option C is correct Answer