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If c o s θ - 1 1 c o s 2 θ 4 3 2 7 7 = 0 , then the number of values of θ in 0,2 π is

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

B. 2

Step-by-step solution

cos ⁡ θ 7 + 1 7 cos ⁡ 2 θ - 6 + 1 7 cos ⁡ 2 θ - 8 = 0 ⇒ 2 cos ⁡ 2 θ + cos ⁡ θ - 2 = 0 ⇒ 4 c o s 2 θ - 2 + cos ⁡ θ - 2 = 0 ⇒ 4 c o s 2 θ + cos ⁡ θ - 4 = 0 ⇒ cos ⁡ θ = - 1 ± 65 8 cos ⁡ θ = - 1 - 65 8 r e j e c t e d , cos ⁡ θ = - 1 + 65 8 Hence, 2 solutions are possible

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