Find x if 3 cosx= 2 sin^2x
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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.
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