We know that, −1 ≤ sin θ ≤ 1 Adding - 2 on both side, we get ⇒−2 − 1 ≤ − 2 + sin θ ≤ − 2 + 1 ⇒−3 ≤ − 2 + sin θ ≤ − 1 If we take mod inequality will be changed. ⇒ | − 3 | ≤ | − 2 + sin θ | ≤ | − 1 | ∴ 1 ≤ | − 2 + sin θ | ≤ 3 Hence, the maximum value of |-2 + sin θ| is 3.