NCERT Class 12 · Ch 2 Exercise 2.2 · Q5
NCERT Class 12 Maths · Chapter 2 Inverse Trigonometric Functions · Exercise 2.2 Question 5
Simplify tan⁻¹((cos x−sin x)/(cos x+sin x)), −π/4<x<3π/4.
💡 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: π/4−x
- The denominator cos x+sin x is nonzero inside the stated interval.
- The quotient is tan(π/4−x), using the tangent difference identity (also valid by sine/cosine forms when cos x=0).
- The angle π/4−x lies in (−π/2,π/2), so the principal inverse gives π/4−x.
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