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CBSE Class 12 Mathematics 2026 Main Paper 65/2/3 · Q335 Marksinverse_cosine_domain

CBSE Class 12 Mathematics 2026 Main Paper 65/2/3 · Question 33 (Inverse Trigonometric Functions)

Find the domain of q(x)=arccos(4x²−3), solve q(x)=0, and find the range of 3q(x)−π.

✅ Step-by-Step Solution

Final Answer: Domain [−1,−1/√2]∪[1/√2,1]; x=±1; range [−π,2π].
  1. Require −1≤4x²−3≤1, so 1/2≤x²≤1. This gives the two domain intervals.
  2. Take cosine in q(x)=0 to get 4x²−3=1, so x=±1.
  3. On the domain the argument covers [−1,1], so q covers [0,π]. Scaling and shifting gives [−π,2π].

📋 CBSE Stepwise Marking Scheme

  • [1 mark] Require −1≤4x²−3≤1, so 1/2≤x²≤1. This gives the two domain intervals.
  • [3 marks] Take cosine in q(x)=0 to get 4x²−3=1, so x=±1.
  • [1 mark] On the domain the argument covers [−1,1], so q covers [0,π]. Scaling and shifting gives [−π,2π].

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All Questions in CBSE Class 12 Mathematics 2026 Main Paper 65/2/3

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