Q80.If f(x) = 2 tan−1 x + sin−1( 1+x22x ), x > 1, then f(5) is equal to (1) π 2 (2) tan−1( 15665 ) (3) π (4) 4 tan−1(5)
What This Question Tests
The problem tests the application of inverse trigonometric identities, specifically `sin⁻¹(2x/(1+x²))`, considering the given domain `x > 1`. Correctly identifying the identity in this domain leads to a simplification of the function.
Concepts Tested
Formulas Used
sin⁻¹(2x/(1+x²)) = π - 2tan⁻¹x (for x > 1)
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📋 Question Details
- Chapter
- Inverse Trigonometric Functions
- Topic
- Properties of Inverse Trigonometric Functions
- Year
- 2015
- Shift
- 10 Apr Online
- Q Number
- Q80
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 2: Inverse Trigonometric Functions
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