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Trigonometrical Equations
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સમીકરણ $cosec\, \theta -cot \,\theta = 1$ ના $[0,2 \pi]$ માં ઉકેલોની સંખ્યા ...... મળે
A
$4$
B
$3$
C
$2$
D
$1$
Solution
$\cos ec\theta – \cot \theta = 1 \Rightarrow 1 – \cos \theta = \sin \theta $
$\Rightarrow 2 \sin ^{2} \frac{\theta}{2}=2 \sin \frac{\theta}{2} \cos \frac{\theta}{2}$
$\Rightarrow \sin \frac{\theta}{2}\left(\sin \frac{\theta}{2}-\cos \frac{\theta}{2}\right)=0$
$\because \sin \frac{\theta}{2} \neq 0 \Rightarrow \tan \frac{\theta}{2}=1 \Rightarrow \theta=\frac{\pi}{2}$
Standard 11
Mathematics
