NCERT Class 12 · Ch 2 Exercise 2.2 · Q6
NCERT Class 12 Maths · Chapter 2 Inverse Trigonometric Functions · Exercise 2.2 Question 6
Simplify tan⁻¹(x/√(a²−x²)), |x|<a.
💡 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: sin⁻¹(x/a)
- The hypothesis implies a>0. Set θ=sin⁻¹(x/a)∈(−π/2,π/2).
- Then cos θ=√(a²−x²)/a>0, so tan θ=x/√(a²−x²).
- Principal tan⁻¹ returns θ=sin⁻¹(x/a).
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