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

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

Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

MathematicsInverse Trigonometric FunctionsProperties of ITFMedium2 minPYQ_2020

MathematicsMediumnumerical

If $y = \sum_{k = 1}^{6} k \cos^{- 1} \{\frac{3}{5} \cos k x - \frac{4}{5} \sin k x\}$ then $\frac{d y}{d x}$ at $x = 0$ is

Answer:

91.00

Solution:

For, small values near $0$ , i.e., $|x| < < . . 1$

$y = \sum_{k = 1}^{6} k \cos^{- 1} (\cos k x \cdot \cos α - \sin k x \cdot \sin α)$

$= \sum_{k = 1}^{6} k \cos^{- 1} (\cos (k x + α))$
$= \sum_{k = 1}^{6} k (k x + α)$

$= \sum_{k = 1}^{6} (k^{2} x + k α)$

$\frac{d y}{d x} = \sum_{k = 1}^{6} k^{2} = \frac{6 (7) (13)}{6} = 91$

Stream:JEESubject:MathematicsTopic:Inverse Trigonometric FunctionsSubtopic:Properties of ITF

⏱ 2mℹ️ Source: PYQ_2020

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