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Question Number 48659 by Cheyboy last updated on 26/Nov/18

$$\mathrm{Find}\mathrm{x}$$$$3\sec \left[2(\mathrm{x}+\frac{\pi }{6})\right]=4$$

Answered by ajfour last updated on 26/Nov/18

$$let\theta =x+\frac{\pi }{6}$$$$\Rightarrow \cos 2\theta =3/4$$$$\Rightarrow 2\theta =2n\pi \pm {\cos }^{-1}\frac{3}{4}$$$$x=n\pi -\frac{\pi }{6}\pm \frac{1}{2}{\cos }^{-1}\frac{3}{4}.$$

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