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Trigonometrical Equations
hard
અહી $S=\left[-\pi, \frac{\pi}{2}\right)-\left\{-\frac{\pi}{2},-\frac{\pi}{4},-\frac{3 \pi}{4}, \frac{\pi}{4}\right\}$ આપલે છે. તો ગણ $=\{\theta \in S : \tan \theta(1+\sqrt{5} \tan (2 \theta))=\sqrt{5}-\tan (2 \theta)\}$ ની સભ્ય સંખ્યા $...$ થાય.
A
$0$
B
$5$
C
$3$
D
$4$
(JEE MAIN-2022)
Solution
$\tan \theta+\sqrt{5} \tan 2 \theta \tan \theta=\sqrt{5}-\tan 2 \theta$ $\tan 3 \theta=\sqrt{5}$
$\theta=\frac{ n \pi}{3}+\frac{\alpha}{3} ; \quad \tan \alpha=\sqrt{5}$
Five solution
Standard 11
Mathematics
