Question

What is the maximum value of 3 sin θ - cos θ?
1. √8
2. √10
3. 3
4. √13

Answer 1

Correct Answer - Option 2 : √10

Formula Used:

Basic concept of trigonometric ratio and identities

We know that

Maximum value for expression a sin θ + b cos θ = √(a² + b²)

Calculation:

The expression can also be written as 3 sin θ - cos θ = 3 sin θ + (-1) cos θ

Now, by comparing the given expression with the standard expression the value of a and b are

∴ a = 3 and b = -1

∴ Maximum value = √ (3)² + (-1)² = √10

Hence, option (2) is correct