How do you evaluate the expression 1 – sin(x) – sin(x)?

To evaluate the expression 1 – sin(x) – sin(x), we start by simplifying it.

First, notice that the expression can be simplified as:

• 1 – sin(x) – sin(x) can be rewritten as 1 – 2sin(x).

So the expression now simplifies to:

• 1 – 2sin(x)

This expression expresses the value based on the sine of the angle x. The sine function, sin(x), varies between -1 and 1 for all real numbers x. Therefore:

• If sin(x) = 0, then 1 – 2sin(x) = 1 – 0 = 1.
• If sin(x) = 1, then 1 – 2sin(x) = 1 – 2 = -1.
• If sin(x) = -1, then 1 – 2sin(x) = 1 + 2 = 3.

Thus, the value of the expression 1 – sin(x) – sin(x) (or 1 – 2sin(x)) can vary within the range of [ -1, 3 ] depending on the value of sin(x).

In summary:

• For sin(x) = 0: Result = 1
• For sin(x) = 1: Result = -1
• For sin(x) = -1: Result = 3