NCERT Class 12 · Ch 2 Exercise 2.2 · Q3
NCERT Class 12 Maths · Chapter 2 Inverse Trigonometric Functions · Exercise 2.2 Question 3
Simplify tan⁻¹((√(1+x²)−1)/x), x≠0.
💡 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: (1/2)tan⁻¹x
- Set θ=tan⁻¹x∈(−π/2,π/2); cos θ>0.
- tan(θ/2)=sin θ/(1+cos θ)=x/(√(1+x²)+1)=(√(1+x²)−1)/x.
- Since θ/2∈(−π/4,π/4), taking principal tan⁻¹ gives θ/2.
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