Class 12 Inverse Trigonometric Functions · Short Answer2 Marksprincipal_values
Class 12 Maths · Inverse Trigonometric Functions · Short Answer #88
Evaluate \(\sin(2\sin^{-1}0.6)\).
✅ Step-by-Step Solution
Final Answer: 24/25=0.96
- Let θ=arcsin0.6=arcsin(3/5), so sin θ=3/5.
- The principal θ is acute, hence cos θ=√(1−9/25)=4/5. Apply sin2θ=2sin θ cos θ=2·3/5·4/5.
- Thus the value is 24/25=0.96.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Let θ=arcsin0.6=arcsin(3/5), so sin θ=3/5.
- [1 mark] The principal θ is acute, hence cos θ=√(1−9/25)=4/5. Apply sin2θ=2sin θ cos θ=2·3/5·4/5.
- [0.5 marks] Thus the value is 24/25=0.96.
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