For n in Z , the general solution of the | vedclass

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Question

$(\sqrt{3}-1) \sin 	heta+(\sqrt{3}+1) \cos 	heta=2$

$\Rightarrow \frac{(\sqrt{3}-1)}{2 \sqrt{2}} \sin 	heta+\left(\frac{\sqrt{3}+1}{2 \sqrt{2}}\

Vedclass · Accepted Answer

$	heta \, = \,2n\pi \, \pm \,\frac{\pi }{4}\, + \,\frac{\pi }{{12}}$

Vedclass · Answer

$(\sqrt{3}-1) \sin 	heta+(\sqrt{3}+1) \cos 	heta=2$

$\Rightarrow \frac{(\sqrt{3}-1)}{2 \sqrt{2}} \sin 	heta+\left(\frac{\sqrt{3}+1}{2 \sqrt{2}}ight) \cos 	heta=\frac{1}{\sqrt{2}}$

$\Rightarrow \sin \frac{\pi}{12} \sin 	heta+\cos \frac{\pi}{12} \cos 	heta=\cos \frac{\pi}{4}$

${\Rightarrow \cos \left(	heta-\frac{\pi}{12}ight)=\cos \frac{\pi}{4}} $

${\Rightarrow 	heta-\frac{\pi}{12}=2 \mathrm{n} \pi \pm \frac{\pi}{4}} $

$\quad \left[ {	herefore \cos 	heta  = \cos \alpha  \Rightarrow 	heta  = 2{m{n}}\pi  \pm \alpha } ight]$

$\Rightarrow 	heta=2 n \pi \pm \frac{\pi}{4}+\frac{\pi}{12},$ $n$ is any integer.

For $n \in Z$ , the general solution of the equation

$(\sqrt 3 - 1)\,\sin \,\theta \, + \,(\sqrt 3 + 1)\,\cos \theta \, = \,2$ is

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