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The solution of the equation sin 2 ⁡ x + cos 2 ⁡ 3 x = 1 is

Options

  1. Ax = n π 3
  2. Bx = n π + π 4
  3. Cx = n π 4
  4. Dx = n π + π 2

Correct answer

C. x = n π 4

Step-by-step solution

sin 2 ⁡ x = 1 - cos 2 ⁡ 3 x = sin 2 ⁡ 3 x sin 2 ⁡ 3 x - sin 2 ⁡ x = 0 sin ⁡ 4 x sin ⁡ 2 x = 0 sin ⁡ 2 x = 0 ⇒ 2 x = n π ⇒ x = n π 2 or sin ⁡ 4 x = 0 ⇒ 4 x = n π ⇒ x = n π 4 ⇒ x = n π 4

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