Solve $sec^2 x-3secx + 2=0$ for all solutions [0, 2pi)?

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Answer 1 · 2016-10-14T15:15:29

$sec^2 x-3secx + 2=0$

$=>sec^2 x-2secx-secx + 2=0$

$=>sec x(secx-2)-1(secx - 2)=0$

$=>(secx-2)(secx - 1)=0$

when
$secx-2=0$

$=>secx=2$

$=>cosx=1/2=cos(pi/3)=cos(2pi-pi/3)$

So $x = pi/3 and x= (5pi)/3$

Again when

$" "(secx - 1)=0$

$=>cosx=1=cos(o)" as "0<= x < 2pi$

So $x=0$

Solve sec^2 x-3secx + 2=0 sec^2 x-3secx + 2=0 for all solutions [0, 2pi)?