Determine whether the following statements are true and give an explanation or counterexample.

a. sin (a + b) = sin a + sin b.

b. The equation cos θ = 2 has multiple real solutions.

c. The equation sin θ = 1/2 has exactly one solution.

d. The function sin (πx/12) has a period of 12.

e. Of the six basic trigonometric functions, only tangent and cotangent have a range of (- ∞, ∞).

f. sin^-1 x/cos^-1 x = tan^-1 x.

g. cos^-1 (cos (15π/16)) = 15π/16.

h. sin^-1 x = 1/sin x.