NCERT Class 12 · Ch 2 Miscellaneous Exercise · Q12
NCERT Class 12 Maths · Chapter 2 Inverse Trigonometric Functions · Miscellaneous Exercise Question 12
Solve tan⁻¹((1−x)/(1+x))=(1/2)tan⁻¹x, 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: x=1/√3.
- Let θ=tan⁻¹x∈(0,π/2). The quotient equals tan(π/4−θ).
- Since π/4−θ∈(−π/4,π/4), its principal arctangent is π/4−θ.
- The equation becomes π/4−θ=θ/2, hence θ=π/6.
- Thus x=tan(π/6)=1/√3>0, which satisfies the original equation.
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