In this question, you will be using the following trigonometric identities: 2 cos a + sin a = 1 cos(a + B) sin(a+B) = cos a cossin a sin = sin a cos+ cos a sin 123 (1) (2) (3) where a, ER. You do not need to prove these identities. You may also use without proof the fact that the set {R} COS a sin o is exactly the set of unit vectors in R. Now for any real number a, define : a R cos a - sin a Ra sin a COS a