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

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - Trigonometrical equations4 Marks
MCQ
$\cot \theta = \sin 2\theta (\theta \ne n\pi $, $n$ is integer), if $\theta = $
  • A
    ${45^o}$ and ${60^o}$
  • ✓
    ${45^o}$ and ${90^o}$
  • C
    ${45^o}$only
  • D
    ${90^o}$only
✓

Answer

Correct option: B.
${45^o}$ and ${90^o}$
b
(b) $\cot \theta = \sin 2\theta ,{\rm{ }}(\theta \ne n\pi ) $

$\Rightarrow 2{\sin ^2}\theta \cos \theta = \cos \theta $

$ \Rightarrow $ $\cos \theta = 0$ or ${\sin ^2}\theta = \frac{1}{2} = {\sin ^2}\left( {\frac{\pi }{4}} \right)$

$ \Rightarrow $ $\theta = (2n + 1)\frac{\pi }{2}$ or $\theta = n\pi \pm \frac{\pi }{4}$

$ \Rightarrow $ $\theta = {90^o}$ and ${45^o}$.

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