Class 12 Inverse Trigonometric Functions · Long Answer3 Marksinverse_trigonometric_equations
Class 12 Maths · Inverse Trigonometric Functions · Long Answer #67
Solve \(\sin^{-1}(1-x)-2\sin^{-1}x=\pi/2\).
✅ Step-by-Step Solution
Final Answer: x=0
- The two arcsine domains intersect at x∈[0,1].
- Rearrange to arcsin(1−x)=π/2+2arcsin x. For x∈[0,1] the left side is at most π/2, whereas the right side is at least π/2.
- Equality therefore forces arcsin x=0, hence x=0. Direct substitution gives arcsin1−2arcsin0=π/2.
- The unique solution is x=0.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] The two arcsine domains intersect at x∈[0,1].
- [1 mark] Rearrange to arcsin(1−x)=π/2+2arcsin x. For x∈[0,1] the left side is at most π/2, whereas the right side is at least π/2.
- [1 mark] Equality therefore forces arcsin x=0, hence x=0. Direct substitution gives arcsin1−2arcsin0=π/2.
- [0.5 marks] The unique solution is x=0.
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