Question

(i) 2 cos0 - 3 cose + 1 = 0 369, 0-0​

Answer 1

Answer:

Step-by-step explanation:

My question is, "Is there any specific domain for given equation?"

f(β) = 2cos²β - 3cosβ + 1 = 0

Let x = cosβ

Rewrite the equation

2t² - 3t + 1 = 0

2t² - 2t - t + 1 = 0

2t(t - 1) - (t - 1) = 0

(t - 1)(2t - 1) = 0 ⇒ $t_{1}$ = 1 and $t_{2}$ = $\frac{1}{2}$

cosβ = $\frac{1}{2}$ ⇒ β ∈ { ... - 5π/3, - π/3, π/3, 5π/3, 7π/3 ... } = A

cosβ = 1 ⇒ β ∈ { .... - 2π, 0, 2π, ... } = B

Thus, β ∈ A ∪ B