For - π 2 ≤ x ≤ π 2 , the number of points of intersection of curves y = cos ⁡ x and y = sin ⁡ 3 x is

Step-by-step solution

y = cos ⁡ x ;   y = sin ⁡ 3 x ⇒ cos ⁡ x = c o s π 2 - 3 x ⇒ x = 2 n π ± π 2 - 3 x ⇒ 4 x = 2 n π + π 2 ,   - 2 x = 2 n π - π 2 ⇒ x = n π 2 + π 8 ,   x = k π + π 4 ⇒ x = 4 n + 1 π 8 ,   x = 4 k + 1 π 4 n = 0 ⇒ x = π 8 , k = 0 ⇒ x = π 4 n = - 1 ⇒ x = - 3 π 8 ⇒ x = - 3 π 8 , π 8 and π 4