Using the definition of modulus function, we have the following two cases: CASE 1: If 2−sinθ≥0⇒2≥sinθ, then: |2−sinθ|=2−sinθ In order to maximize 2−sinθ,sinθ should be minimum. The minimum value of sinθ is -1 . ∴ The maximum value of 2−sinθ is 2−(−1)=3. CASE 2: If 2−sinθ<0⇒2<sinθ, which is not possible.Therefore, the maximum value of |2−sinθ| is |3|=3.