Question

Find the general solution for the equation cos 4x =cos 2x.

Answer 1

cos4x = cos2x

Using formula : cos2a = 2cos²a - 1

2cos²2x - 1 = cos2x ⇒ 2cos²2x - cos2x -1 = 0
⇒ 2cos²2x - 2cos2x + cos2x - 1 = 0
⇒ 2cos2x(cos2x-1 ) + 1 (cos2x-1) = 0
⇒ (cos2x-1)(2cos2x + 1) = 0
⇒ cos2x = 1
⇒ 2x = 2nπ +- 0  ⇒ x = nπ

or        cos2x = -1/2
⇒ 2x = 2nπ +- 2π/3 ⇒ x  = nπ +- π/3

Intersection : x ∈ nπ U nπ +- π/3

Hope my answer is correct.

Answer 2

Answer:

here is your answer mate

Step-by-step explanation:

2cos²2x - 1 = cos2x ⇒ 2cos²2x - cos2x -1 = 0

⇒ 2cos²2x - 2cos2x + cos2x - 1 = 0

⇒ 2cos2x(cos2x-1 ) + 1 (cos2x-1) = 0

⇒ (cos2x-1)(2cos2x + 1) = 0

⇒ cos2x = 1

and

⇒ 2x = 2nπ +- 0  ⇒ x = nπ

cos2x = -1/2

⇒ 2x = 2nπ +- 2π/3 ⇒ x  = nπ +- π/3