Question Number 48659 by Cheyboy last updated on 26/Nov/18
![Find x 3sec[2(x+(π/6))]= 4](Q48659.png)
$$\mathrm{Find}\:\mathrm{x} \\ $$$$\mathrm{3sec}\left[\mathrm{2}\left(\mathrm{x}+\frac{\pi}{\mathrm{6}}\right)\right]=\:\mathrm{4} \\ $$
Answered by ajfour last updated on 26/Nov/18
$${let}\:\:\theta={x}+\frac{\pi}{\mathrm{6}} \\ $$$$\Rightarrow\:\:\mathrm{cos}\:\mathrm{2}\theta\:=\:\mathrm{3}/\mathrm{4} \\ $$$$\Rightarrow\:\:\mathrm{2}\theta\:=\:\mathrm{2}{n}\pi\pm\mathrm{cos}^{−\mathrm{1}} \frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\:\:\:\:\:\:{x}\:=\:{n}\pi−\frac{\pi}{\mathrm{6}}\pm\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}^{−\mathrm{1}} \frac{\mathrm{3}}{\mathrm{4}}\:. \\ $$