Prove $\cos \left( x - \frac { \pi } { 2 } \right) + \cos \left( x + \frac { \pi } { 2 } \right) = 0$

Essay

Prove $\cos \left( x - \frac { \pi } { 2 } \right) + \cos \left( x + \frac { \pi } { 2 } \right) = 0$ .