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JEE Main20202 Sep 2020Evening ShiftMathematicsInverse Trigonometric FunctionsActual

If y = ∑ k = 1 6 k cos - 1 3 5 cos k x - 4 5 sin k x then d y d x at x = 0 is

Correct answer

91

Step-by-step solution

For, small values near 0 , i.e., x < < . . 1 y = ∑ k = 1 6 k cos - 1 cos k x · cos α - sin k x · sin α = ∑ k = 1 6 k cos - 1 cos k x + α = ∑ k = 1 6 k k x + α = ∑ k = 1 6 k 2 x + k α d y d x = ∑ k = 1 6 k 2 = 6 7 13 6 = 91

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