Question

Please answer this question with step by step working out, 50 points

Answer 1

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 = $\frac{1}{2}$ ⇒ 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