Question

Find the principal and general solutions of the following equation.
sec x=2

Answer 1

Here, sec x = 2 $\Rightarrow cosx=\frac{1}{2}$, which is positive, so x lies in first or fourth quadrant.

cos x = $\frac{1}{2}=cos{60}^0$ or cos $({360}^0-{60}^0)$

= cos ${60}^0$ or cos ${300}^0$

= cos $\frac{\pi }{3}$ or cos$\frac{5\pi }{3}$

Hence the principal solutions are $\frac{\pi }{3},\frac{5\pi }{3}$.

Now cos x = cos $\frac{\pi }{3}$

$\Rightarrow x=2n\pi \pm \frac{\pi }{3}$ where~ $nϵZ$.