NCERT Class 12 · Ch 2 Exercise 2.2 · Q4
NCERT Class 12 Maths · Chapter 2 Inverse Trigonometric Functions · Exercise 2.2 Question 4
Simplify tan⁻¹√((1−cos x)/(1+cos x)), 0<x<π.
💡 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/2
- The half-angle identity gives (1−cos x)/(1+cos x)=tan²(x/2).
- Here 0<x/2<π/2, so the nonnegative square root is tan(x/2).
- The principal arctangent returns x/2.
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