Question

Sin(3pi/14)-sin(pi/14)-sin(5pi/14)

Answer 1

Sin3π/14-(sinπ/14+sin5π/14)=sin3π/14-2sin3π/14cosπ87=sin3π/14(1-2cosπ/7)

Answer 2

To compute the value of the expression sin(3π/14) - sin(π/14) - sin(5π/14), we'll use the trigonometric identity:

sin(A - B) = sin(A)cos(B) - cos(A)sin(B)

Let's break down the expression step by step:

1. sin(3π/14) - sin(π/14) - sin(5π/14)

2. We can rewrite sin(5π/14) as sin(π - 3π/14) since sin(π - θ) = sin(θ).

3. Using the trigonometric identity, sin(A - B) = sin(A)cos(B) - cos(A)sin(B), we get:

sin(5π/14) = sin(π)cos(3π/14) - cos(π)sin(3π/14) = 0 * cos(3π/14) - (-1) * sin(3π/14) = sin(3π/14)

4. Now, the expression becomes:

sin(3π/14) - sin(π/14) - sin(3π/14)

5. Since sin(3π/14) is present with both positive and negative signs, they cancel out:

Result = -sin(π/14)

Therefore, the value of the expression is -sin(π/14).