Question

Solve $\sec 4\theta -\sec 2\theta =2$

• A. $\theta =(n+\frac{1}{8})\pi$, $nϵZ$
• B. $\theta =(n+\frac{1}{4})\pi$, $nϵZ$
• C. $\theta =(n+\frac{1}{3})\pi$, $nϵZ$
• D. $\theta =(n+\frac{1}{2})\pi$, $nϵZ$

Answer 1

The correct option is D $\theta =(n+\frac{1}{2})\pi$, $nϵZ$

We have, $\frac{1}{\cos 4\theta }-\frac{1}{\cos 2\theta }=2$

$\cos 2\theta -\cos 4\theta =2\cos 2\theta \cos 4\theta =\cos 2\theta +\cos 6\theta$

$\cos 6\theta +\cos 4\theta =0$

$2\cos 5\theta \cos \theta =0$

$\Rightarrow$ $\cos 5\theta =0$ or $\cos \theta =0$

$\Rightarrow$ $5\theta =(2n+1)\frac{\pi }{2}$ or

$\theta =(2n+1)\frac{\pi }{2}$, $n\in Z$

$\theta =(n+\frac{1}{2})\frac{\pi }{5}$ or $\theta =(n+\frac{1}{2})\pi$, $n\in Z$