Idenities Example

I have decided to use an example of one Double Angle Identity, and on example of a Sum and Difference Identity..

1) Find the exact value of the following:
a. sin (π/12) =sin (π/3-π/4) = sin(π/3) cos(π/4) - cos(π/3) sin(π/4)
= (√3/2)(√2/2) - (1/2)(√2/2)
= (√6/4) - (√2/4)
final answer = (√6 - √4)/4

2) Solve for "x" where 0° ≤ x ≤ 360°

a. sin2(x) = sin(x)

2sin(x) cos(x) = sin(x)
2sin(x) cos(x) - sin(x) = 0
sin(x) (2cos(x) - 1) = 0

sin(x) = 0, therefore x = 0, 180, 360

2cos(x) - 1 = 0

cos (x) = 1/2, therefore x = 60, 300