Question

Why is cos(nπ) = (–1)n true, when n could be any integer?

Answer 1

its true because -1 to even power is positive, -1 to odd power is negative

Answer 2

Given,
`cos\,n\pi=(-1)^n`

We state why it is true.

Lets check for some values of n.

for n = 0

⇒
`cos\,0=(-1)^0=1`

for n = 1

⇒
`cos\,\pi=(-1)^1=-1`

for n = -1

⇒
`cos\,-\pi=(-1)^{-1)=-1`

for n = 2

⇒
`cos\,2\pi=(-1)^{2)=1`

for n = -2

⇒
`cos\,-2\pi=(-1)^{-2)=1`

So, Its clear from above . value of cos nπ is either 1 or -1.

value of cos nπ is 1 when n is even integer and -1 when n is odd integer.