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

45°

tan²x - 3tanx + 2 - 0

tan²x - 2tanx - tanx + 2 - 0

tanx ( tanx - 2 ) - 1 ( tanx - 2 ) = 0

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

Either ( tanx - 1 = 0  ) or ( tanx - 2 = 0  )

tanx - 2 = 0  is not possible

So, tanx - 1 = 0

tanx = 1

{ We know, tan45º = 1 }

So ,  x = 45º 

45º