Q85.Let x = sin(2 tan−1 α) and y = sin( 12 tan−1 43 ). If S = {α ∈R : y2 = 1 −x}, then ∑α∈S 16α3 is equal to _______.
What This Question Tests
This question tests the ability to simplify expressions involving inverse trigonometric functions using appropriate identities and then solve the resulting algebraic equation to find the values of alpha.
Concepts Tested
Formulas Used
sin(2 tan^-1 x) = 2x / (1+x^2)
sin(A/2) = sqrt((1-cos A)/2)
tan(theta) = 4/3 => sin(theta) = 4/5, cos(theta) = 3/5
cos(2 tan^-1 x) = (1-x^2) / (1+x^2)
📚 NCERT Sections This Tests
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Chemistry Class 12 · Chapter 8
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Physics Class 11 · Chapter 2
2.1 Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
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Chemistry Class 11 · Chapter 1
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📋 Question Details
- Chapter
- Inverse Trigonometric Functions
- Topic
- Trigonometric identities and inverse trigonometric functions
- Year
- 2022
- Shift
- 25 Jul Shift 2
- Q Number
- Q85
- Type
- Numerical
- NCERT Ref
- Class 12 Mathematics Ch 2: Inverse Trigonometric Functions, Class 11 Mathematics Ch 3: Trigonometric Functions
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