Q237 / 270 · NDA 2021 (Phase 2) · Mathematics

If $y=\cos x \cdot \cos 4 x \cdot \cos 8 x$, then what is $\frac{1}{y} \frac{d y}{d x}$ at $x=\frac{\pi}{4}$ equal to?

  • Correct answer
    A
    -1
  • B
    0
  • C
    1
  • D
    3

Solution

$\begin{aligned} & y=\cos x \cdot \cos 4 x \cdot \cos 8 x \\ & \ln y=\ln (\cos x)+\ln (\cos 4 x)+\ln (\cos 8 x) \\ & \frac{1}{y} \frac{d y}{d x}=-\tan x-4 \tan 4 x-8 \tan 8 x \end{aligned}$ Put $x=\frac{\pi}{4}$ $\frac{1}{y} \frac{d y}{d x}=-1-4(0)-8(0)-1$

Hence, the correct answer is option: 'A'.

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