UPSC NDA Math Model Paper 5

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.