Solve for x: sin^2x - 4 sin x + 3 = 0, 0 ≤ x ≤ (π)/2

sin²x - 4 sinx + 3 = 0

sin²x - 3 sinx  - sinx + 3 = 0

sinx ( sinx - 3 ) - 1 ( sinx - 3 ) = 0

( sinx - 1 ) ( sinx - 3 ) = 0

Either sinx - 1 = 0 or sinx - 3 = 0

Sinx - 3 = 0 is not possible

So, sinx - 1 = 0

sinx = 1

{ we know, sin 90º = 1 }

So, x = 90º

= \(\frac{π}{2}\)