The number of distinct solutions of sec theta | vedclass

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(A) Given equation: $\sec 	heta + 	an 	heta = \sqrt{3}$$\Rightarrow \frac{1}{\cos 	heta} + \frac{\sin 	heta}{\cos 	heta} = \sqrt{3}$$\Rightarrow

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$1$

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(A) Given equation: $\sec 	heta + 	an 	heta = \sqrt{3}$$\Rightarrow \frac{1}{\cos 	heta} + \frac{\sin 	heta}{\cos 	heta} = \sqrt{3}$$\Rightarrow 1 + \sin 	heta = \sqrt{3} \cos 	heta$ (where $\cos 	heta 
eq 0$)$\Rightarrow \sqrt{3} \cos 	heta - \sin 	heta = 1$Dividing by $2$ on both sides:$\Rightarrow \frac{\sqrt{3}}{2} \cos 	heta - \frac{1}{2} \sin 	heta = \frac{1}{2}$$\Rightarrow \cos 	heta \cos \frac{\pi}{6} - \sin 	heta \sin \frac{\pi}{6} = \cos \frac{\pi}{3}$$\Rightarrow \cos \left(	heta + \frac{\pi}{6}ight) = \cos \frac{\pi}{3}$General solution: $	heta + \frac{\pi}{6} = 2n\pi \pm \frac{\pi}{3}, n \in Z$Case $1$: $	heta = 2n\pi + \frac{\pi}{3} - \frac{\pi}{6} = 2n\pi + \frac{\pi}{6}$For $n=0$,$	heta = \frac{\pi}{6}$ (Valid,$\cos \frac{\pi}{6} 
eq 0$)For $n=1$,$	heta = 2\pi + \frac{\pi}{6} = \frac{13\pi}{6}$ (Outside range $[0, 2\pi]$)Case $2$: $	heta = 2n\pi - \frac{\pi}{3} - \frac{\pi}{6} = 2n\pi - \frac{\pi}{2}$For $n=1$,$	heta = 2\pi - \frac{\pi}{2} = \frac{3\pi}{2}$At $	heta = \frac{3\pi}{2}$,$\cos 	heta = 0$,so $\sec 	heta$ and $	an 	heta$ are undefined.Thus,the only valid solution in $[0, 2\pi]$ is $	heta = \frac{\pi}{6}$.The number of distinct solutions is $1$.

The number of distinct solutions of $\sec \theta + \tan \theta = \sqrt{3}$ for $0 \leqslant \theta \leqslant 2\pi$ is:

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