The sum of the roots of the equation 3 cos ⁡ x - sin ⁡ x = 2 in 0,4 π is k π , then the value of 6 k is

Step-by-step solution

3 cos ⁡ x - sin ⁡ x = ± 2 3 2 cos ⁡ x - 1 2 sin ⁡ x = ± 1 c o s x + π 6 = ± 1 ⇒ x + π 6 = n π ⇒ x = n π - π 6 ⇒ x = π - π 6 , 2 π - π 6 , 3 π - π 6 , 4 π - π 6 ⇒ The sum of roots is 10 π - 2 π 3 = 28 3 π ⇒ 6 k = 6 × 28 3 = 56