The exact value of sin(15 degrees) is sqrt (2 – sqrt(3)) / 2. So, the correct answer is option b.

Here's the step-by-step solution:

1. We know that sin(15 degrees) = sin(45 degrees - 30 degrees).

2. Using the formula for sin(a - b), which is sin(a)cos(b) - cos(a)sin(b), we get sin(45 degrees)cos(30 degrees) - cos(45 degrees)sin(30 degrees).

3. Substituting the known values, we get (sqrt(2)/2 * sqrt(3)/2) - (sqrt(2)/2 * 1/2).

4. Simplifying this, we get sqrt(6)/4 - sqrt(2)/4.

5. Taking sqrt(2)/4 common, we get sqrt(2)/4 * (sqrt(3) - 1), which simplifies to sqrt (2 – sqrt(3)) / 2.

Question

The exact value of sin(15 degrees) is sqrt (2 – sqrt(3)) / 2. So, the correct answer is option b.

Here's the step-by-step solution:

1. We know that sin(15 degrees) = sin(45 degrees - 30 degrees).

2. Using the formula for sin(a - b), which is sin(a)cos(b) - cos(a)sin(b), we get sin(45 degrees)cos(30 degrees) - cos(45 degrees)sin(30 degrees).

3. Substituting the known values, we get (sqrt(2)/2 * sqrt(3)/2) - (sqrt(2)/2 * 1/2).

4. Simplifying this, we get sqrt(6)/4 - sqrt(2)/4.

5. Taking sqrt(2)/4 common, we get sqrt(2)/4 * (sqrt(3) - 1), which simplifies to sqrt (2 – sqrt(3)) / 2.

Knowee AI · Accepted Answer

The exact value of sin(15 degrees) is sqrt (2 – sqrt(3)) / 2. So, the correct answer is option b.

Here's the step-by-step solution:

1. We know that sin(15 degrees) = sin(45 degrees - 30 degrees).

2. Using the formula for sin(a - b), which is sin(a)cos(b) - cos(a)sin(b), we get sin(45 degrees)cos(30 degrees) - cos(45 degrees)sin(30 degrees).

3. Substituting the known values, we get (sqrt(2)/2 * sqrt(3)/2) - (sqrt(2)/2 * 1/2).

4. Simplifying this, we get sqrt(6)/4 - sqrt(2)/4.

5. Taking sqrt(2)/4 common, we get sqrt(2)/4 * (sqrt(3) - 1), which simplifies to sqrt (2 – sqrt(3)) / 2.

What is the exact value of sin (15 degrees)?Question 6Select one:a..380b.sqrt (2 – sqrt(3)) / 2c.sqrt (2 + sqrt (3)) / 2d..350e.Impossible