Find the principal and general solution of the equation: sec x = … - Vidyadip

Question

Find the principal and general solution of the equation: sec x = 2

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Answer

Here sec x = 2 $ \Rightarrow \cos x = \frac{1}{2}$, which is positive, so x lies in first or fourth quadrant.
$\cos \;x = \frac{1}{2} = \cos 60$ or cos ($360^{\circ}-60^{\circ}$)
= cos $60^{\circ}$ or cos $300^{\circ} = \cos \frac{\pi }{3}$ or $\cos \frac{{5\pi }}{3}$
Hence the principal solutions are $\frac{\pi }{3},\frac{{5\pi }}{3}$.
Now $\cos = \cos \frac{\pi }{3} \Rightarrow x = 2\pi \pm \frac{\pi }{3}$ where $n \in Z$

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