Use an addition or subtraction formula to find the exact value of

Question

sin(165°)=√A((√B)-1)/4

 

A=

B=

Answer 1

sin165° = sin(135° + 30°)

 

            = sin135°cos30° + cos135°sin30°

 

            = (√2/2)(√3/2) + (-√2/2)(1/2) = (√6 - √2)/4

Answer 2

Use the half-angle identity.

 

sin(x/2) = √((1 - cosx) / 2)

 

sin(330/2) = √((1 - cos(330) / 2)

 

                = √((1 - √(3)/2) / 2)

 

 

               = √(2 - 2√3)           1

                  __________  *   _____   

                          √2                √2

 

 

              = √(2 - 2√3) / 2

 

              = √(2(1 - √2)) / 2