Answer:
x = 30°, 90°, 150°
Step-by-step explanation:
Using the trigonometric identity
sin2x = 2sinxcosx
Given
sin2x- cosx = 0, then
2sinxcosx - cosx = 0 ← factor out cosx from each term
cosx(2sinx - 1) = 0
Equate each factor to zero and solve for x
cosx = 0 ⇒ x = 90°
2sinx - 1 = 0 ⇒ 2sinx = 1 ⇒ sinx = [tex]\frac{1}{2}[/tex] ⇒ x = 30° ← first quadrant
sinx > 0 in first/ second quadrant, thus
x = (180 - 30)° = 150° ← second quadrant
x = 30°, x = 90°, x = 150° for 0 ≤ x ≤ 180
