NCERT Class 12 · Ch 2 Miscellaneous Exercise · Q14
NCERT Class 12 Maths · Chapter 2 Inverse Trigonometric Functions · Miscellaneous Exercise Question 14
Solve sin⁻¹(1−x)−2sin⁻¹x=π/2.
💡 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: C: x=0.
- The two inverse sines require x∈[−1,1] and 1−x∈[−1,1], whose intersection is [0,1].
- For x∈[0,1], sin⁻¹(1−x)≤π/2 and 2sin⁻¹x≥0. Equality of their difference with π/2 forces sin⁻¹x=0 and sin⁻¹(1−x)=π/2.
- Thus x=0; direct substitution confirms it. Select C.
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