Class 12 Inverse Trigonometric Functions · Short Answer2 Marksprincipal_values
Class 12 Maths · Inverse Trigonometric Functions · Short Answer #45
Evaluate \(\tan^{-1}[2\sin(2\cos^{-1}(\sqrt3/2))]\).
✅ Step-by-Step Solution
Final Answer: π/3
- The principal value arccos(√3/2)=π/6.
- Thus 2sin(2arccos(√3/2))=2sin(π/3)=√3.
- The expression is arctan√3=π/3.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] The principal value arccos(√3/2)=π/6.
- [1 mark] Thus 2sin(2arccos(√3/2))=2sin(π/3)=√3.
- [0.5 marks] The expression is arctan√3=π/3.
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