## sin(A-B)

### In trigonometry, sin(A – B) refers to the sine function of the difference between angles A and B

In trigonometry, sin(A – B) refers to the sine function of the difference between angles A and B. It is important to note that the sine function of an angle represents the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle.

To calculate sin(A – B), we can use a trigonometric identity called the angle subtraction formula. The formula is as follows:

sin(A – B) = sin(A)cos(B) – cos(A)sin(B)

This formula allows us to find the sine of the difference between two angles by combining the sines and cosines of those angles.

Let’s understand it through an example:

Suppose we have A = 30 degrees and B = 45 degrees. We can use the angle subtraction formula to find sin(A – B):

sin(A – B) = sin(30)cos(45) – cos(30)sin(45)

To find the values of sin(30), cos(30), sin(45), and cos(45), we can refer to the trigonometric values of common angles. In this case, sin(30) = 0.5, cos(30) = √3/2, sin(45) = √2/2, and cos(45) = √2/2. Substituting these values into the formula, we get:

sin(30 – 45) = (0.5)(√2/2) – (√3/2)(√2/2)

Simplifying further:

sin(30 – 45) = (√2/4) – (√6/4)

Thus, sin(30 – 45) = (√2 – √6)/4.

Therefore, the sine of the difference between 30 degrees and 45 degrees is (√2 – √6)/4.

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