If 1 a^2 ^2x + b^2 ^2x dx = 1 12 ^ -1 (3 x) + constant, then the maximum value of a sin x + b cos x, is:

JEE Main 2024 Mathematics question

If + constant, then the maximum value of a sin x + b cos x, is:

Answer: (A)

The integral is (1/ab)tan⁻¹(a tan x/b), so ab = 12 and a/b = 3, giving a = 6,

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Question ID VK-012136