Q78.The value of tan−1[ √1+x2−√1+x2+ √1−x2√1−x2 ], (1) π 4 + 21 cos−1x2 (2) π4 −cos−1x2 (3) π 4 −12 cos−1x2 (4) π4 + cos−1x2
What This Question Tests
This question tests the ability to simplify inverse trigonometric expressions by using a suitable trigonometric substitution and applying trigonometric identities. It requires careful algebraic manipulation of square roots and recognition of the tangent addition/subtraction formula.
Concepts Tested
Formulas Used
x² = cosθ
1 + cosθ = 2cos²(θ/2)
1 - cosθ = 2sin²(θ/2)
tan(π/4 - A) = (1 - tanA) / (1 + tanA)
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📋 Question Details
- Chapter
- Inverse Trigonometric Functions
- Topic
- Properties of Inverse Trigonometric Functions
- Year
- 2017
- Shift
- 08 Apr Online
- Q Number
- Q78
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 2: Inverse Trigonometric Functions
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