Class 12 Inverse Trigonometric Functions · Short Answer2 Marksprincipal_values
Class 12 Maths · Inverse Trigonometric Functions · Short Answer #47
Evaluate \(\sin^{-1}[\cos(43\pi/5)]\).
✅ Step-by-Step Solution
Final Answer: −π/10
- Reduce 43π/5=8π+3π/5, so the cosine equals cos3π/5.
- Write cos3π/5=sin(π/2−3π/5)=sin(−π/10).
- Since −π/10 lies in the arcsine principal interval, the value is −π/10.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Reduce 43π/5=8π+3π/5, so the cosine equals cos3π/5.
- [1 mark] Write cos3π/5=sin(π/2−3π/5)=sin(−π/10).
- [0.5 marks] Since −π/10 lies in the arcsine principal interval, the value is −π/10.
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