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STD 11 - Trigonometrical equations — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - Trigonometrical equations4 Marks
MCQ
If $\sec x\cos 5x + 1 = 0$, where $0 < x < 2\pi $, then $x =$
  • A
    $\frac{\pi }{5},\frac{\pi }{5}$
  • B
    $\frac{\pi }{5}$
  • ✓
    $\frac{\pi }{4}$
  • D
    None of these
✓

Answer

Correct option: C.
$\frac{\pi }{4}$
c
(c) $\sec x\cos 5x = - 1 \Rightarrow \cos 5x = - \cos x$

$ \Rightarrow $ $5x = 2n\pi \pm (\pi - x)$

$ \Rightarrow $ $x = \frac{{(2n + 1)\pi }}{6}{\rm{ or }}\frac{{(2n - 1)\pi }}{4}$

Hence $x = \frac{\pi }{4},\,\frac{\pi }{2},\,\frac{{3\pi }}{4},\,\frac{{5\pi }}{6},\,\frac{{5\pi }}{4},\,\frac{{7\pi }}{6},\,\frac{{7\pi }}{4},\,\frac{{9\pi }}{6},\,\frac{{11\pi }}{6}$.

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