Q76.If the sum of all the solutions of + cot−1( 1−x22x ) tan−1( 1−x22x ) = π3 , −1 < x < 1, x ≠0, is α − √34 , then α is equal to _____ .
What This Question Tests
This question involves simplifying an equation using properties and identities of inverse trigonometric functions and then solving for x within the given domain to find the sum of solutions.
Concepts Tested
Formulas Used
tan⁻¹x + cot⁻¹x = π/2
cot⁻¹x = tan⁻¹(1/x) for x>0
2tan⁻¹x = tan⁻¹(2x/(1-x²))
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📋 Question Details
- Chapter
- Inverse Trigonometric Functions
- Topic
- Properties of inverse trigonometric functions
- Year
- 2023
- Shift
- 25 Jan Shift 1
- Q Number
- Q76
- Type
- Numerical
- NCERT Ref
- Class 12 Mathematics Ch 2: Inverse Trigonometric Functions
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