Respuesta :

LammettHash
This is because when [tex]n[/tex] is odd, i.e. [tex]n=2k+1[/tex] for integers [tex]k[/tex], you have

[tex]\cos(\pm\pi)=\cos(\pm3\pi)=\cdots=\cos(\pm(2k+1)\pi)=-1[/tex]

while for even [tex]n[/tex], i.e. when [tex]n=2k[/tex], you have

[tex]\cos0=\cos(\pm2\pi)=\cos(\pm4\pi)=\cdots=\cos(\pm2k\pi)=1[/tex]

Meanwhile, [tex](-1)^n=-1[/tex] is [tex]n[/tex] is odd, while [tex](-1)^n=1[/tex] if [tex]n[/tex] is even.
boffeemadrid

Answer:

True

Step-by-step explanation:

The value of [tex]cosn{\pi}=(-1)^n[/tex] is true as:

when n is odd that is of the form [tex]n=2m+1[/tex] where m is any integer, thus we have

[tex]cos(\pm\pi)=cos(\pm3\pi)=...=cos(\pm(2m+1)\pi=-1[/tex]

and when n is even that is of the form [tex]n=2m[/tex], where m is any integer, thus we have

[tex]cos0=cos(\pm2\pi)=....=cos(\pm2m\pi)=1[/tex]

Thus,  [tex](-1)^n=-1[/tex] for when n is odd and [tex](-1)^n=1[/tex] when n is even.

Hence, the given statement is true.