1. Show that cos^2 x is an even function.

Question

1. Show that cos² x is an even function. 
2. Evaluate \(\int\limits_{-\frac{π}{4}}^{\frac{π}{4}} cos^2xdx\) 

Answer 1

1. Let f(x) = cos²x ⇒ f(-x) = cos² (-x) = cos² x = f(x) even.

2.