Question

The general solution(s) of $\theta$ satisfying the equation ${\tan }^2\theta +\sec 2\theta =1$ can be (where $n\in Z$)

• A. $n\pi$
• B. $n\pi \pm \frac{\pi }{3}$
• C. $n\pi \pm \frac{\pi }{4}$
• D. $\frac{n\pi }{2}$

Answer 1

Answer: (A), (B)

$n\pi \pm \frac{\pi }{3}$

${\tan }^2\theta +\sec 2\theta =1$
Let $t=\tan \theta$
$t^2+\frac{1+t^2}{1-t^2}=1$
$\Rightarrow t^2(t^2-3)=0\Rightarrow \tan \theta =0,\pm \sqrt{3}\Rightarrow \theta =n\pi \text{or}\theta =n\pi \pm \frac{\pi }{3},n\in Z.$