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Trigonometrical Equations
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જ્યારે $x \in\left[0, \frac{\pi}{2}\right]$ હોય ત્યારે સમીકરણ $\sqrt{3}\left(\cos ^{2} x\right)=(\sqrt{3}-1) \cos x+1,$ નાં ઉકેલોની સંખ્યા .......... છે.
A
$1$
B
$2$
C
$3$
D
$4$
(JEE MAIN-2021)
Solution
$\sqrt{3}(\cos x)^{2}-\sqrt{3} \cos x+\cos x-1=0$
$\Rightarrow(\sqrt{3} \cos x+1)(\cos x-1)=0$
$\Rightarrow \cos x=1$ or $\cos x=-\frac{1}{\sqrt{3}}$ (reject)
$\Rightarrow x=0$ only
Standard 11
Mathematics
