Question

Find the exact value of sin(11pi/12)cos(pi/6)-cos(11pi/12)sin(pi/6)

Answer 1

The exact value of sin(11pi/12)cos(pi/6)-cos(11pi/12)sin(pi/6) is 1/2 - 1/2√(2 + √3).

Step-by-step explanation:

To find the exact value of sin(11π/12)cos(π/6)-cos(11π/12)sin(π/6), we can use the trigonometric identity sin(A-B) = sinAcosB - cosAsinB. This will allow us to simplify the expression.

Let's substitute the values for A = 11π/12 and B = π/6:

1. Sin(11π/12 - π/6) = sin(5π/12) = ½√(2 - √3)
2. Cos(11π/12 - π/6) = cos(5π/12) = ½√(2 + √3)

Now we can substitute these values into the expression:

Sin(11π/12)cos(π/6) - cos(11π/12)sin(π/6) = ½√(2 - √3) * ½ - ½√(2 + √3) * ½

Simplifying further, we get: ½ - ½√(2 + √3)

Answer 2

We use the identity sin (A - B) = sin A cos B - cos B sin A

so the above = sin (11pi/12 - pi/6) = sin 3pi/4 = 1 / sqrt2 answer