JEE PYQ: Inverse Trigonometric Functions Question 11
Question 11 - 2020 (02 Sep Shift 2)
If $y = \sum_{k=1}^{6} k\cos^{-1}\left{\frac{3}{5}\cos kx - \frac{4}{5}\sin kx\right}$, then $\frac{dy}{dx}$ at $x = 0$ is ______.
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Answer: 91
Solution
Let $\cos a = \frac{3}{5}$, $\sin a = \frac{4}{5}$. Then $y = \sum_{k=1}^{6} k\cos^{-1}{\cos(kx + a)} = \sum_{k=1}^{6} k(kx + a)$. So $\frac{dy}{dx} = \sum_{k=1}^{6} k^2 = \frac{6 \cdot 7 \cdot 13}{6} = 91$.
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