The solution of the equation tan 2 ⁡ x - 1 - 1 = 1 + cos ⁡ 2 x is

Step-by-step solution

1 tan 2 ⁡ x - 1 = 1 + cos ⁡ 2 x ⇒ cos 2 ⁡ x sin 2 ⁡ x - cos 2 ⁡ x = 1 + cos ⁡ 2 x ⇒ 1 + cos ⁡ 2 x 2 - cos ⁡ 2 x - 1 + cos ⁡ 2 x = 0 1 + cos ⁡ 2 x - 1 2 cos ⁡ 2 x - 1 = 0 ⇒ 1 + cos ⁡ 2 x = 0 or 1 + 1 2 cos ⁡ 2 x = 0 ⇒ cos ⁡ 2 x = - 1 or - 1 2 ⇒ 2 x = 2 n π ± π or 2 n π ± 2 π 3 ⇒ x = n π ± π 2 or n π ± π 3 But for x = n π ± π 2 , cos ⁡ x = 0 and hence tan ⁡ x is not defined ⇒ x = n π ± π 3