Use a sum or difference identity to find the exact value of

Use a sum or difference identity to find the exact value of the expression. 11x 12 sin 11 12 sin (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) Enter your answer in the answer box. 0 Type here to search

Solution

sin(11pi/12) = sin(11*180/12)

            = sin(165)

          = sin(180-15)

             = sin(15)

             = sin(45-30)

         = sin(45). cos(30)-cos(45)sin(30)

     = (1/sqrt(2))*(sqrt(3)/2)- (1/sqrt(2))(1/2)

=(sqrt(3)-1)/(2sqrt(2))