Class 12 Inverse Trigonometric Functions · Short Answer2 Marksbranch_sensitive_simplification
Class 12 Maths · Inverse Trigonometric Functions · Short Answer #60
For \(-\pi/4<x<\pi/4\), simplify \(\sin^{-1}[(\sin x+\cos x)/\sqrt2]\).
✅ Step-by-Step Solution
Final Answer: x+π/4
- Use (sin x+cos x)/√2=sin(x+π/4).
- The domain gives 0<x+π/4<π/2, inside the principal arcsine interval.
- Thus the expression equals x+π/4.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Use (sin x+cos x)/√2=sin(x+π/4).
- [1 mark] The domain gives 0<x+π/4<π/2, inside the principal arcsine interval.
- [0.5 marks] Thus the expression equals x+π/4.
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