The number of solutions of the equation 3 + cos ⁡ x 2 = 4 - 2 sin 8 ⁡ x in 0 , 9 π is equal to

Step-by-step solution

- 1 ≤ cos ⁡ x ≤ 1 ⇒ 2 ≤ 3 + cos ⁡ x ≤ 4 ⇒ 4 ≤ 3 + cos ⁡ x 2 ≤ 16 Also, - 1 ≤ sin ⁡ x ≤ 1 ⇒ 0 ≤ 2 sin 8 ⁡ x ≤ 2 ⇒ 2 ≤ 4 - 2 sin 8 ⁡ x ≤ 4 so, equality is possible when L H S = R H S = 4 ⇒ cos ⁡ x = - 1 and sin ⁡ x = 0 ⇒ x = ( 2 n + 1 ) π ⇒ x = π , 3 π , 5 π , 7 π