Verified answer

Note that cos²(x) = 1 - sin²(x). Then, we obtain:

3sin(x) = 2(1 - sin²(x))

3sin(x) = 2 - 2sin²(x)

2sin²(x) + 3sin(x) - 2 = 0

Factoring..

(2sin(x) - 1)(sin(x) + 2) = 0

Zero-product property...

2sin(x) - 1 = 0 and sin(x) + 2 = 0

sin(x) = ½ [No existing x values for sin(x) + 2 = 0 since -2 is not within -1 ≤ n ≤ 1]

x = arcsin(½)

x = 30°, 150° [A]

I hope this helps!

3sin x = 2cos^2 x = 2(1 - sin^2 x) = 2 - 2sin^2 x

=> 2sin^2 x + 3sin x - 2 = 0

=> 2sin^2 x + 4sin x - sin x - 2 = 0

=> 2sin x(sin x + 2) - 1(sin x + 2) = 0

=> (2sin x - 1)(sin x + 2) = 0

=> 2sin x = 1, sin x = -2 (impossible)

=> sin x = 1/2

=> x = sin-1 (1/2) = 30, 150

{51.3317, 128.668} Deg