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JEE Main 2022 Mathematics question

MathematicsDifferential EquationJEE Main 2022

Let S = (0, Extra open brace or missing close brace2\pi ) - {\pi /2, , , Extra close brace or missing open brace7\pi /4}. Let y = y(x), x S, be the solution curve of the differential equation dy/dx = 1/(1 + sin 2x), . If the sum of abscissas of all the points of intersection of the curve y = y(x) with the curve sin x is , then k is equal to .

Answer: 42

Solution

1 + sin 2x = (sin x + cos , so dy = dx/(1 + tan , giving y = −1/(1 + tan x) + c. With : c = 1, so y = tan x/(1 + tan x) = sin x/(sin x + cos x). Setting this equal to sin x:

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Question ID VK-025373