Finding the Limit of (cos(Pi/2x))^2x when x is ∞

[Frank Einstein]

Homework Statement

I have a problem, I don't know how to find the limit (cos(Pi/2x))^2x when x is ∞

Homework Equations

(1+(1/x))^(1/x)=e

The Attempt at a Solution

I have been looking for solutions on the internet, but most of these just tend to be for fractions, I don't know how to operate with a cosine.
Any help?

 

[jedishrfu]

Have you tried inserting numbers like x as 1,10,100... To see how the formula trends that might give you an idea of what happens as x gets larger?

Do you know the value of cos(0) or cos(PI/2) ?

You need to show us some work before we can help further.