Class 12 Inverse Trigonometric Functions · Long Answer3 Marksprincipal_values
Class 12 Maths · Inverse Trigonometric Functions · Long Answer #100
Evaluate \(2\cos^{-1}(1/2)+2\sin^{-1}(-1/2)-\cos^{-1}(-1)\).
✅ Step-by-Step Solution
Final Answer: −2π/3
- The principal values are arccos(1/2)=π/3, arcsin(−1/2)=−π/6 and arccos(−1)=π.
- Substitute to obtain 2π/3+2(−π/6)−π.
- This simplifies to 2π/3−π/3−π=π/3−π.
- The correct value is −2π/3.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] The principal values are arccos(1/2)=π/3, arcsin(−1/2)=−π/6 and arccos(−1)=π.
- [1 mark] Substitute to obtain 2π/3+2(−π/6)−π.
- [1 mark] This simplifies to 2π/3−π/3−π=π/3−π.
- [0.5 marks] The correct value is −2π/3.
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