Question

Select the general solution(s) of the trigonometric equation
$\sec \theta =-1.$

• A. $\theta =(2n+1)\pi \forall n\in Z$
• B. $\theta =(2n+1)\frac{\pi }{2}\forall n\in Z$
• C. $\theta =2n\pi \forall n\in Z$
• D. $\theta =n\pi \forall n\in Z$

Answer 1

The correct option is A $\theta =(2n+1)\pi \forall n\in Z$

Given that
$\sec \theta =-1$
$\Rightarrow \frac{1}{\cos \theta }=-1$
$\Rightarrow \cos \theta =-1$

We know that $\cos \theta =-1\Rightarrow \theta =(2n+1)\pi \forall n\in Z$

$\therefore$ the general solution of $\sec \theta =-1$ is
$\theta =(2n+1)\pi \forall n\in Z$