Class 12 Inverse Trigonometric Functions · Short Answer2 Marksbranch_sensitive_simplification
Class 12 Maths · Inverse Trigonometric Functions · Short Answer #57
For \(-3\pi/2<x<\pi/2\), simplify \(\tan^{-1}[\cos x/(1-\sin x)]\).
✅ Step-by-Step Solution
Final Answer: π/4+x/2
- The half-angle identity gives cos x/(1−sin x)=tan(π/4+x/2); the denominator is nonzero on the stated open interval.
- The interval implies −π/2<π/4+x/2<π/2, so this angle lies in the principal arctangent range.
- Thus the expression equals π/4+x/2.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] The half-angle identity gives cos x/(1−sin x)=tan(π/4+x/2); the denominator is nonzero on the stated open interval.
- [1 mark] The interval implies −π/2<π/4+x/2<π/2, so this angle lies in the principal arctangent range.
- [0.5 marks] Thus the expression equals π/4+x/2.
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