Q79.Considering only the principal values of inverse functions, the set A = {x ≥0 : tan−1(2x) + tan−1(3x) = π4 } (1) Is an empty set (2) Contains more than two elements (3) Contains two elements (4) Is a singleton
What This Question Tests
The problem requires applying the sum formula for inverse tangent functions and then solving the resulting algebraic equation, while also considering the domain condition for the formula to be valid (xy < 1) and the given condition x ≥ 0.
Concepts Tested
Formulas Used
tan⁻¹(x) + tan⁻¹(y) = tan⁻¹((x+y)/(1-xy)) for xy < 1
📚 NCERT Sections This Tests
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14.2 Which of the statements given in Exercise 14.1 is true for p-type semiconductos.
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9.15 Apply mirror equation and the condition: (a) f < 0 (concave mirror); u < 0 (object on left) (b) f > 0; u < 0 (c) f > 0 (convex mirror) and u < 0 (d) f < 0 (concave mirror); f < u < 0 to deduce the desired result.
📋 Question Details
- Chapter
- Inverse Trigonometric Functions
- Topic
- Properties of inverse trigonometric functions
- Year
- 2019
- Shift
- 12 Jan Shift 1
- Q Number
- Q79
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 2: Inverse Trigonometric Functions
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