If sec^2 x - 3 sec x + 2 = 0, then the value of x(0 < x < 90°) is :

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

sec²x - 2.secx - secx + 2 = 0

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

(secx - 1).(secx - 2) = 0

Either secx - 1 = 0  OR secx - 2 = 0

{ secx - 1 = 0 not possible because 0 < x < 90°.}

So,  secx - 2 = 0

secx = 2

{ we know, sec60° = 2 }

so, x = 60°