NCERT Class 12 · Ch 2 Miscellaneous Exercise · Q13
NCERT Class 12 Maths · Chapter 2 Inverse Trigonometric Functions · Miscellaneous Exercise Question 13
For |x|<1, evaluate sin(tan⁻¹x).
💡 Concept Hints
- Recall the principal range of the inverse function before simplifying.
- Find an angle with the required trigonometric value, then verify it belongs to the principal range.
✅ Step-by-Step Solution
Final Answer: D: x/√(1+x²).
- Set θ=tan⁻¹x∈(−π/2,π/2), so cos θ>0.
- Then cos θ=1/√(1+x²) and sin θ=tan θ cos θ=x/√(1+x²). Select D.
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