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Question Number 78946 by mathocean1 last updated on 21/Jan/20

$$\mathrm{solve}$$$$\cos x-\sqrt{3}sinx=1$$

Commented by msup trace by abdo last updated on 21/Jan/20

$$e\iff 2(\frac{1}{2}cosx-\frac{\sqrt{3}}{2}sinx)=1\Rightarrow$$$$cos\left(\frac{\pi }{3}\right)cosx-sin\left(\frac{\pi }{3}\right)sinx=\frac{1}{2}$$$$\Rightarrow cos(x+\frac{\pi }{3})=cos\left(\frac{\pi }{3}\right)\Rightarrow$$$$x+\frac{\pi }{3}=\frac{\pi }{3}+2k\pi orx+\frac{\pi }{3}=\frac{2\pi }{3}+2k\pi \left(kfromZ\right)$$$$\Rightarrow x=3k\pi or=\frac{\pi }{3}+2k\pi$$

Commented by msup trace by abdo last updated on 21/Jan/20

$$erroroftypox=2k\pi orx=\frac{\pi }{3}+2k\pi$$

Answered by Mr. AR last updated on 31/Jan/20

$$cos(90°-x)-\sqrt{3}sinx=1$$$$sinx-\sqrt{3}sinx=1$$$$sinx(1-\sqrt{3})=1$$$$sinx=\frac{1}{1-\sqrt{3}}\times \frac{1+\sqrt{3}}{1+\sqrt{3}}$$$$sinx=\frac{1+1.732}{1-3}$$$$sinx=\frac{2.732}{-2}$$$$\mathit{s}\mathit{i}\mathit{n}\mathit{x}=-1.366$$

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