2.51 () www The various trigonometric identities used in the discussion of periodic variables in this chapter can be proven easily from the relation exp(iA) = cosA + i sinA (2.296)

in which i is the square root of minus one. By considering the identity exp(iA) exp(−iA) = 1 (2.297)

prove the result (2.177). Similarly, using the identity cos(A − B) =

exp{i(A − B)} (2.298)

where denotes the real part, prove (2.178). Finally, by using sin(A − B) = exp{i(A − B)}, where denotes the imaginary part, prove the result (2.183).