Question

Find the principal and general solution of the equation $\sec x=2$.

Answer 1

$\sec x=2$

We know, $\sec \frac{\pi }{3}=2$ and $\sec \frac{5\pi }{3}=\sec (2\pi -\frac{\pi }{3})=\sec \frac{\pi }{3}=2$.

Therefore, the principal solutions are $x=\frac{\pi }{3}$ and $\frac{5\pi }{3}$.

Now, $\sec x=\sec \frac{\pi }{3}$

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

$x=2n\pi \pm \frac{\pi }{3}$, where $n\in Z$.

Therefore, the general solution is $x=2n\pi \pm \frac{\pi }{3},n\in Z$.