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CBSE Class 12 Mathematics 2026 Main Paper 65/2/2 · Q325 Marksinverse_sine_domain

CBSE Class 12 Mathematics 2026 Main Paper 65/2/2 · Question 32 (Inverse Trigonometric Functions)

For p(x)=arcsin(1−2x²), find its domain, solve p(x)=π/6 and give the range of 2p(x)+π/2.

✅ Step-by-Step Solution

Final Answer: Domain [−1,1], x=±1/2, range [−π/2,3π/2].
  1. Require −1≤1−2x²≤1, giving 0≤x²≤1.
  2. Taking sine in p(x)=π/6 gives 1−2x²=1/2, so x=±1/2.
  3. On the domain the argument covers [−1,1]. Scale the principal range [−π/2,π/2] by two and add π/2.

📋 CBSE Stepwise Marking Scheme

  • [1 mark] Require −1≤1−2x²≤1, giving 0≤x²≤1.
  • [3 marks] Taking sine in p(x)=π/6 gives 1−2x²=1/2, so x=±1/2.
  • [1 mark] On the domain the argument covers [−1,1]. Scale the principal range [−π/2,π/2] by two and add π/2.

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All Questions in CBSE Class 12 Mathematics 2026 Main Paper 65/2/2

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