How is sin (5π/4) - cos (5π/4) = 0

Question

In the question verify rolles theorem for the function f(x) = e^x ( sin x - cos x ) on [π/4, 5π/4],

I can't understand why sin (5π/4) - cos (5π/4)=0?

Answer 1

Use a unit circle (or a calculator) and you'll see:

sin ^5π/₄ = - ^√2/₂

cos ^5π/₄ = - ^√2/₂

So what you'll get is

- ^√2/₂ - (- ^√2/₂ ) = - ^√2/₂ + ^√2/₂ = 0