If y( ) = 2 + 2 3 + 4 2 + 5 + 2 , then at θ = 2, y″ + y′ + y is equal to:

JEE Main 2024 Mathematics question

If , then at θ = , y″ + y′ + y is equal to:

Answer: (D)

With c = cos θ the denominator is 4c³ + 8c² + 2c − 2 = 2(c + 1)(2c² + 2c − 1) and the numerator is 2c² + 2c − 1, so y = 1/(2(1 + cos θ)).

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Question ID VK-011656