Class 12 Inverse Trigonometric Functions · Short Answer2 Marksprincipal_values
Class 12 Maths · Inverse Trigonometric Functions · Short Answer #46
Evaluate \(\cos^{-1}[\cos(2\pi/3)]+\sin^{-1}[\sin(2\pi/3)]\).
✅ Step-by-Step Solution
Final Answer: π
- Since 2π/3∈[0,π], arccos(cos2π/3)=2π/3.
- For arcsine, sin(2π/3)=sin(π/3), with π/3 in its principal interval; that term is π/3.
- The sum is 2π/3+π/3=π.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Since 2π/3∈[0,π], arccos(cos2π/3)=2π/3.
- [1 mark] For arcsine, sin(2π/3)=sin(π/3), with π/3 in its principal interval; that term is π/3.
- [0.5 marks] The sum is 2π/3+π/3=π.
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