Evaluate the difference by using a product formula Sin11 pi1

Evaluate the difference by using a product formula. Sin(11 pi/12) - sin(5 pi/12)

Solution

sin(11pi/12) - sin(5pi/12)

Use formula :: sinx - siny = 2cos[(x+y)/2]sin[(x -y)/2]

sin(11pi/12) - sin(5pi/12) = 2cos[(11pi/12+5pi/12)/2]sin[(6pi/12)/2]

= 2cos(2pi/3)sin(pi/4)

= 2(-1/2)(1/sqrt2)

= -1/sqrt2