Answer:
This result can be verified using a trigonometric identity.
Step-by-step explanation:
We use the the trigonometric identity
[tex]cos(a\:{\pm}\:b)=cos(a)*cos(b){\mp}sin(a)*sin(b).[/tex]
In our case [tex]a=x[/tex] and [tex]b=\pi /2[/tex], thus:
[tex]cos(x+\frac{\pi}{2} )=cos(x)*cos(\frac{\pi}{2})-sin(x)*sin(\frac{\pi}{2}).[/tex]
Since
[tex]cos(\frac{\pi}{2})=0[/tex] and
[tex]sin(\frac{\pi}{2})=1[/tex]
the above equation simplifies as
[tex]cos(x+\frac{\pi}{2} )=cos(x)*cos(\frac{\pi}{2})-sin(x)*sin(\frac{\pi}{2})=-sin(x)[/tex]
[tex]\boxed{cos(x+\frac{\pi}{2} )=-sin(x)}[/tex]
thus proving the identity.
