Question

The solution of $Sec4\theta -Sec2\theta =2$ is

• A. $n\pi +\frac{\pi }{2}$
• B. $($2 $n+1)\frac{\pi }{2}$ , $(2n+1)\frac{\pi }{10}$
• C. $($2 $n+1)\frac{\pi }{10}$
• D. $($2 $n+1)\frac{\pi }{2}$

Answer 1

The correct option is B $($2 $n+1)\frac{\pi }{2}$ , $(2n+1)\frac{\pi }{10}$

given equation is
$\frac{1}{cos4\theta }-\frac{1}{cos2\theta }=2$
$\frac{1}{2t^2-1}-\frac{1}{t}=2$ where $t=cos2\theta$
this gives $(4t^2-2t-1)(t+1)=0$
$t=-1$ or $t=\frac{1\pm \sqrt{5}}{4}$

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