How can we simplify 1 – sin(x)?

To simplify the expression 1 – sin(x), we can look for a way to rewrite it in a more manageable form. One common approach in trigonometry is to express the sine function in terms of cosine, or to use Pythagorean identities.

The sine function is related to the cosine function through the identity:

• sin²(x) + cos²(x) = 1

From this, we can rearrange it to express 1 as:

• 1 = cos²(x) + sin²(x)

Thus, we can replace 1 in our expression:

• 1 – sin(x) = cos²(x) + sin²(x) – sin(x)

However, the expression 1 – sin(x) itself does not simplify directly to a simpler expression without additional context or restrictions on x. It’s a standard form and represents the value subtracted by the sine of x, graphed in terms of sine.

Therefore, in its simplest form, 1 – sin(x) remains as it is unless we are evaluating at specific points or need further manipulation in relation to other trigonometric expressions.