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CBSE Class 12 Mathematics 2026 Main Paper 65/2/1 · Q345 Marksinverse_cosine_domain

CBSE Class 12 Mathematics 2026 Main Paper 65/2/1 · Question 34 (Inverse Trigonometric Functions)

Find the domain of g(x)=arccos(x²−1), solve g(x)=π/3, and give the range of a nonprincipal inverse cosine branch.

✅ Step-by-Step Solution

Final Answer: [−√2,√2]. The solutions are ±√(3/2). One nonprincipal range is [−π,0].
  1. Require −1≤x²−1≤1, so 0≤x²≤2 and |x|≤√2.
  2. Take cosine in g(x)=π/3 to get x²−1=1/2, giving x=±√(3/2).
  3. Cosine is one-to-one from [−π,0] onto [−1,1], so [−π,0] is the range of one nonprincipal inverse.

📋 CBSE Stepwise Marking Scheme

  • [1 mark] Require −1≤x²−1≤1, so 0≤x²≤2 and |x|≤√2.
  • [3 marks] Take cosine in g(x)=π/3 to get x²−1=1/2, giving x=±√(3/2).
  • [1 mark] Cosine is one-to-one from [−π,0] onto [−1,1], so [−π,0] is the range of one nonprincipal inverse.

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All Questions in CBSE Class 12 Mathematics 2026 Main Paper 65/2/1

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