Question

Find the general solution of the following equation :
$2{\cos }^2\theta -5\cos \theta +2=0$

Answer 1

${2\cos }^2\theta -5\cos \theta +2=0$

$\Rightarrow {2\cos }^2\theta -4\cos \theta -\cos \theta +2=0$

$\Rightarrow 2\cos \theta (\cos \theta -2)+(\cos \theta -2)=0$

$\Rightarrow (2\cos \theta -1)(\cos \theta -2)=0$

$\therefore$ $\cos \theta =1/2⟶\left(1\right)$ or $\cos \theta =2⟶\left(2\right)$

Equation $\left(2\right)$ is not possible, Since $\cos \theta ϵ[-1,1]$

From equation $\left(1\right)$

$\cos \theta =1/2$

We know that if $\cos \theta =\cos \alpha$

$\theta =2n\pi \pm \alpha$

$nϵZ$

$\therefore$ $\cos \theta =1/2=\cos {60}^0=\cos \pi /3$

$\theta =2n\pi \pm \frac{\pi }{3};nϵZ$