Question

Find x if 3 cosx= 2 sin^2x

Answer 1

Answer:

2nπ +- π/3

Step-by-step explanation:

Here 3 cos(x) = 2sin²(x)

⇒ 3 cos(x) = 2*(1-cos²(x))

⇒ 3 cos(x) = 2 - 2cos²(x)

⇒ 2cos²(x) + 3cos(x) -2 = 0

⇒ cos(x) = 1/2 or -2

Since cos(x) ∈ [-1, 1] cos(x) cannot be - 2. Hence

cos(x) = 1/2 = cos(π/3)

⇒ x = 2nπ +- π/3

where n is any integer.